九州大学 研究者情報
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増田 弘毅(ますだ ひろき) データ更新日:2019.06.20



主な研究テーマ
確率過程に関する統計推測理論の開発とその実装
キーワード:統計的漸近理論,確率過程,大規模高頻度従属データ解析
2000.04.
従事しているプロジェクト研究
先端的確率統計学が開く大規模従属性モデリング
2014.10, 代表者:吉田朋広, 東京大学大学院数理科学研究科, JST(日本)
従属性のあるビッグデータへの統計的モデリングと、確率統計学の原理に則った統計解析の体系化を目指します。とくに、超高頻度金融データ解析を可能とする確率統計的方法を構築し、金融市場のモデリングを通じて、金融技術分野に貢献します。また、時系列データ科学のインフラとなる確率過程に対する統計解析およびシミュレーションのためのソフトウエアを発展させるとともに、SNSのデータ解析による様々な社会的事象の将来予測への応用を行います。(http://www.jst.go.jp/kisoken/crest/project/1111084/14532201.html).
YUIMA project: simulation and inference of multidimensional stochastic differential equations
2012.05~2012.05, 代表者:Stefano Iacus, University of Milan


URL: https://r-forge.r-project.org/projects/yuima/.
研究業績
主要原著論文
1. Alexandre Brouste, Hiroki Masuda, Efficient estimation of stable Lévy process with symmetric jumps, Statistical Inference for Stochastic Processes, 10.1007/s11203-018-9181-0, 1-19, 2018.03, [URL], Efficient estimation of a non-Gaussian stable Lévy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a non-singular Fisher information matrix through the use of a non-diagonal norming matrix. The asymptotic normality and efficiency of a sequence of roots of the associated likelihood equation are shown as well. Moreover, we show that a simple preliminary method of moments can be used as an initial estimator of a scoring procedure, thereby conveniently enabling us to bypass numerically demanding likelihood optimization. Our simulation results show that the one-step estimator can exhibit quite similar finite-sample performance as the maximum likelihood estimator..
2. Shoichi Eguchi, Hiroki Masuda, Schwarz type model comparison for LAQ models, Bernoulli, 10.3150/17-BEJ928, 24, 3, 2278-2327, 2018.08, [URL], For model-comparison purpose, we study asymptotic behavior of the marginal quasi-log likelihood associated with a family of locally asymptotically quadratic (LAQ) statistical experiments. Our result entails a far-reaching extension of applicable scope of the classical approximate Bayesian model comparison due to Schwarz, with frequentist-view theoretical foundation. In particular, the proposed statistics can deal with both ergodic and non-ergodic stochastic process models, where the corresponding M-estimator may of multi-scaling type and the asymptotic quasi-information matrix may be random. We also deduce the consistency of the multistage optimal-model selection where we select an optimal sub-model structure step by step, so that computational cost can be much reduced. Focusing on some diffusion type models, we illustrate the proposed method by the Gaussian quasi-likelihood for diffusion-type models in details, together with several numerical experiments..
3. 上原悠槙, 増田弘毅, Levy駆動型確率微分方程式の段階的推定について, 統計数理, 65, 1, 21-38, 65, no.1, 21--38, 2017.04, 非正規型Levy過程で駆動される確率微分方程式 (SDE) モデルの推定を考える. 指数的エルゴード性とデータの高頻度性の下, 正規型疑似スコア関数に基づいてスケール係数およびドリフト係数をこの順に段階的に推定する方法を提案し, 推定量の漸近正規性および裾確率評価を導出する. 推定対象を分割することで最適化の計算負荷が削減され, より安定した推定精度が得られる. 拡散過程の場合と異なり, 特に両係数のパラメータが共通因子を持つ場合には, ドリフト係数の漸近共分散行列は同時推定の場合と異なる形をとる..
4. Dmytro Ivanenko, Alexey M. Kulik, Hiroki Masuda, Uniform LAN property of locally stable Lévy process observed at high frequency, ALEA - Latin American Journal of Probability and Mathematical Statistics, 12, 835-862, 2015.10, [URL], Suppose we have a high-frequency sample from the {¥lp} of the form $X_t^¥theta=¥beta t+¥gamma Z_t+U_t$, where $Z$ is a possibly asymmetric locally $¥al$-stable {¥lp}, and $U$ is a nuisance {¥lp} less active than $Z$. We prove the LAN property about the explicit parameter $¥theta=(¥beta,¥gam)$ under very mild conditions without specific form of the {¥lm} of $Z$, thereby generalizing the LAN result of ¥cite{AJ07}. In particular, it is clarified that a non-diagonal norming may be necessary in the truly asymmetric case. Due to the special nature of the local $¥al$-stable property, the asymptotic Fisher information matrix takes a clean-cut form..
5. Hiroki Masuda, Convergence of Gaussian quasi-likelihood random fields for ergodic Levy driven SDE observed at high frequency, Annals of Statistics, 10.1214/13-AOS1121, 41, 3, 1593-1641, 2013.06.
6. Hiroki Masuda, Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes, Stochastic Processes and their Applications, 10.1016/j.spa.2013.03.013, 123, 7, 2752-2778, 2013.07, The purpose of this paper is to derive the stochastic expansion of self-normalized-residual functionals stemming from a class of diffusion type processes observed at high frequency, where total observing period may or may not tend to infinity. The result enables us to construct some explicit statistics for goodness of fit tests, consistent against “presence of a jump component” and “diffusion-coefficient misspecification”; then, the acceptance of the null hypothesis may serve as a collateral evidence for using the correctly specified diffusion type model. Especially, our asymptotic result clarifies how to remove the bias caused by plugging in a diffusion-coefficient estimator..
7. Hiroki Masuda, Reiichiro Kawai, Local asymptotic normality for normal inverse Gaussian Levy processes with high-frequency sampling, ESAIM: Probability and Statistics, 10.1051/ps/2011101, 17, 13-32, 2013.01, We prove the local asymptotic normality for the full parameters of the normal inverse Gaussian Lévy process X, when we observe high-frequency data XΔn,X2Δn,...,XnΔn with sampling mesh Δn → 0 and the terminal sampling time nΔn → ∞. The rate of convergence turns out to be (√nΔn, √nΔn, √n, √n) for the dominating parameter (α,β,δ,μ), where α stands for the heaviness of the tails, β the degree of skewness, δ the scale, and μ the location. The essential feature in our study is that the suitably normalized increments of X in small time is approximately Cauchy-distributed, which specifically comes out in the form of the asymptotic Fisher information matrix..
8. Hiroki Masuda, Approximate self-weighted LAD estimation of discretely observed ergodic ornstein-uhlenbeck processes, Electronic Journal of Statistics, 10.1214/10-EJS565, 4, 525-565, 2010.01, [URL], We consider drift estimation of a discretely observed OrnsteinUhlenbeck process driven by a possibly heavy-tailed symmetric Lévy process with positive activity index β. Under an infill and large-time sampling design, we first establish an asymptotic normality of a self-weighted least absolute deviation estimator with the rate of convergence being √ nh1−1/β n, where n denotes sample size and hn > 0 the sampling mesh satisfying that hn → 0 and nhn → ∞. This implies that the rate of convergence is determined by the most active part of the driving Lévy process; the presence of a driving Wiener part leads to √ nhn, which is familiar in the context of asymptotically efficient estimation of diffusions with compound Poisson jumps, while a pure-jump driving Lévy process leads to a faster one. Also discussed is how to construct corresponding asymptotic confidence regions without full specification of the driving Lévy process. Second, by means of a polynomial type large deviation inequality we derive convergence of moments of our estimator under additional conditions..
9. Hiroki Masuda, Joint estimation of discretely observed stable L\'evy processes with symmetric L\'evy density, The Journal of The Japan Statistical Society, Vol.39, no.1, pp.49-75, 2009.06.
10. Hiroki Masuda, Ergodicity and exponential β-mixing bounds for multidimensional diffusions with jumps, Stochastic Processes and their Applications, 10.1016/j.spa.2006.04.010, 117, 1, 35-56, 2007.01, [URL], Let X be a multidimensional diffusion with jumps. We provide sets of conditions under which: X fulfils the ergodic theorem for any initial distribution; and X is exponentially β-mixing. Utilizing the Foster-Lyapunov drift criteria developed by Meyn and Tweedie, we extend several existing results concerning diffusions. We also obtain the boundedness of moments of g (Xt) for a suitable unbounded function g. Our results can cover a wide variety of diffusions with jumps by selecting suitable test functions, and serve as fundamental tools for statistical analyses concerning the processes..
11. Hiroki Masuda, Simple estimators for parametric Markovian trend of ergodic processes based on sampled data, Journal of the Japan Statistical Society, 35, no.2, 147-170, 2005.01.
12. Hiroki Masuda, Nakahiro Yoshida, Asymptotic expansion for Barndorff-Nielsen and Shephard's stochastic volatility model, Stochastic Processes and their Applications, 10.1016/j.spa.2005.02.007, 115, 7, 1167-1186, 115, 1167-1185., 2005.01.
主要総説, 論評, 解説, 書評, 報告書等
1. Hiroki Masuda, Approximate quadratic estimating function for discretely observed Lévy driven SDEs with application to a noise normality test, RIMS Kokyuroku, RIMS Kokyuroku 1752 (2011), 113--131., 2011.07.
主要学会発表等
1. Hiroki Masuda, Non-constant scale effect in stable quasi-likelihood inference, ASC2019, Asymptotic Statistics and Computations, 2019.01, [URL], We consider estimation of a locally stable heteroskedastic model based on infill asymptotics. Asymptotic mixed normality of the stable quasi-likelihood estimator is deduced, with explicit and consistently estimable asymptotic random covariance matrix and with diagonal rate matrix..
2. Hiroki Masuda, Locally stable regression with unknown activity index, CMStatistics 2018, 2018.12, Typically, transition of large-scale dependent data, such as those sampled at ultra high-frequency, are highly non-Gaussian. One of natural ways of modeling such data would be to use continuous-time stochastic processes driven by a non-Gaussian pure-jump noise. The related existing literature is, however, still far from being well-developed. In this talk, we present tailor-made quasi-likelihood inference results that can efficiently handle such locally and highly non-Gaussian statistical models with the activity index of the driving noise process being unknown. The model setup includes not only Markovian stochastic differential equations but also a class of semimartingale regression models. Of primary interest are cases where estimation target includes not only the rapidly varying scale structure but also the slowly varying trend one..
3. Alexandre Brouste, Hiroki Masuda, Efficient estimation of stable Lévy process, ASC2018, Asymptotic Statistics and Computations, 2018.02.
4. Alexandre Brouste, Hiroki Masuda, Efficient estimation of stable Lévy process from high-frequency data, Workshop: Infinitely divisible processes and related topics", 2017.12.
5. Hiroki Masuda, Local limit theorem in non-Gaussian quasi-likelihood inference, Asymptotic Statistics of Stochastic Processes and Applications XI, 2017.07, We consider parameter estimation of the finite-dimensional parameter in the stochastic differential equation (SDE) model driven by a highly non-Gaussian noise. We will present handy sufficient conditions for the L1-local limit theorem with convergence rate, which is the key assumption for the asymptotic mixed normality. The sufficient conditions are given only in terms of the driving Levy measure and/or the characteristic exponent of the driving noise. Specific examples satisfying them include stable, exponentially tempered $¥beta$-stable, and generalized hyperbolic Levy processes..
6. Hiroki Masuda, Stable quasi-likelihood regression, EcoSta 2017, 2017.06.
7. Hiroki Masuda, Shoichi Eguchi, Yuma Uehara, Lévy SDE inference in Yuima package, Dynstoch meeting 2017, 2017.04.
8. Hiroki Masuda, Locally stable regression without ergodicity and finite moments, Hokkaido International Symposium "Recent Developments of Statistical Theory in Statistical Science", 2016.10.
9. Hiroki Masuda, On Asymptotics of multivariate non-Gaussian quasi-likelihood, World Congress in Probability and Statistics, 2016.07, We consider (semi-)parametric inference for a class of stochastic differential equation (SDE) driven by a locally stable Levy process, focusing on multivariate setting and some computational aspects. The process is supposed to be observed at high frequency over a fixed time domain. This setting naturally gives rise to a theoretically fascinating quasi-likelihood which brings about a novel unified estimation strategy for targeting a broad spectrum of driving Levy processes. The limit experiment is mixed normal with a clean-cut random information structure, based on which it is straightforward to make several conventional asymptotic statistical decisions. The infill-asymptotics adopted here makes the popular Gaussian quasi-likelihood useless, while instead enabling us not only to incorporate any exogenous and/or observable endogenous data into the trend and/or scale coefficients without essential difficulty, but also to sidestep most crucial assumptions on the long-term stability such as ergodicity and moment boundedness. The proposed quasi-likelihood estimator is asymptotically efficient in some special cases..
10. Hiroki Masuda, On Asymptotics of multivariate non-Gaussian quasi-likelihood, The 4th Institute of Mathematical Statistics Asia Pacific Rim Meeting, 2016.06.
11. Hiroki Masuda, Lévy in quasi-likelihood estimation of SDE, Statistics for Stochastic Processes and Analysis of High Frequency Data V, 2016.03, [URL], We try to give a clear whole picture about the local stable approximation in estimating a L\'{e}vy driven SDE under infill asymptotics without ergodicity. Our finding here is that the completely analogous strategy as in the local Gauss approximation in estimating a diffusion does a good job, when the activity degree is equal to or greater than 1 (the Cauchy-like case). The proposed estimator is indeed asymptotically efficient in some instances..
12. 増田 弘毅, Lévy driven regression model, 日本統計学会春季大会, 2016.03.
13. Hiroki Masuda, Computational aspects of estimating Lévy driven models, The 9th IASC-ARS conference, 2015.12, We consider estimation problem concerning stochastic differential equations driven by a Levy process with jumps. The model is supposed to be observed at high-frequency, allowing us to incorporate a small-time approximation of the underlying likelihood. An overview of some existing theories based on the Gaussian and non-Gaussian quasi-likelihoods is presented, together with their computational aspects. Also to be demonstrated is how to implement the theory in the YUIMA package: an R framework for simulation and inference of stochastic differential equations..
14. 増田 弘毅, Locally Cauchy SDE model with high-frequency data, 大規模統計モデリングと計算統計II, 2015.09, [URL].
15. Hiroki Masuda, On variants of stable quasi-likelihood for Levy driven SDE, Statistique Asymptotique des Processus Stochastiques X, 2015.03, [URL].
16. 増田 弘毅, ジャンプ課程と非正規型擬似尤度, 統計関連学会連合大会, 2014.09.
17. Hiroki Masuda, On sampling problem for pure-jump SDE , 3rd APRM, Taipei, 2014.07, [URL].
18. Hiroki Masuda, LAD-based estimation of locally stable Ornstein-Uhlenbeck processes, Waseda International Symposium on "Stable Process, Semimartingale, Finance & Pension Mathematics", 2014.03, [URL], The LAD type estimator for discretely observed Levy driven OU process is much more efficient than the LSE type one. We prove that the proposed estimator under a random norming is asymptotically standard-normally distributed, making construction of confidence intervals easy..
19. Hiroki Masuda, Stable quasi-likelihood: Methodology and computational aspects, ERCIM 2013 London, 2013.12, [URL], We consider the semi-parametric model described by the parametric locally stable pure-jump stochastic differential equation. We wish to estimate the parametric coefficients based on a high-frequency sample over a fixed interval. In this talk, we introduce a novel, tailor-made estimator based on the stable approximation of the one-step transition distribution. Under suitable regularity conditions, it is shown that the proposed estimator is asymptotically mixed-normal. The result reveals that, in case of the stable-like driving Levy process, the proposed estimator is much more efficient than the conventional Gaussian quasi-maximum likelihood estimator, which requires the large-time asymptotics and leads to a slower rates of convergence. Nevertheless, evaluation of the proposed estimator is computationally more involved compared with the Gaussian case. Also discussed in some detail is the computational aspects of the proposed methodology.
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20. Hiroki Masuda, 局所安定分布近似による推定方式, 統計関連学会連合大会, 2013.09, [URL], 確率微分方程式 (SDE) モデルは, 複雑に時間発展する様々な自然・物理現象を記述す るだけでなく, 離散時間モデルを有効に近似する (平滑化する) モデルとしても機能する. 金融・保険分野においても, 微小時間変動の分布が非正規性を呈する事例は数多く, このよ うなデータを扱う際には非正規 Levy 過程で駆動される SDE モデルが有用である. 非正規 Levy 過程で駆動される SDE モデルの推定においては,微小時間増分の正規近似に基づいた擬似最尤法は効率良く機能しないことが知られている.この場合には,正規型擬似尤 度の使用に伴われる多大な情報損失を回避する為,よりテーラーメイドな推定手法が要求される. 本講演では, そのような推定手法を厳密な漸近分布論と共に具現化する..
21. Hiroki Masuda, On statistical inference for Levy-driven models, The 59th World Statistics Congress (WSC), 2013.08, [URL], 保険数理分野では局所安定型確率微分方程式によるモデリングが有用である.モデルを適合させる対象期間を固定しつつ統計的分布論の理論基盤を確保できるという点において,ノイズの非正規性が如実に現れる当該分野での推測問題に新たな視点・展開を与えた..
22. Hiroki Masuda, Estimation of stable-like stochastic differential equations, 29th European Meeting of Statisticians, 2013.07, [URL], We consider the stochastic differential equation of pure-jumps type with parametric coefficients. We wish to estimate the unknown parameters based on a discrete-time but high-frequency sample. A naive way would be to use the Gaussian quasi likelihood. However, although the Gaussian quasi likelihood is known to be well-suited for the case of diffusions, it leads to asymptotically suboptimal estimator in the pure-jump case; in particular, the Gaussian quasi-maximum likelihood estimation inevitably needs a large-time asymptotics. In this talk, we will introduce another kind of quasi-maximum likelihood estimator based on the local-stable approximation of the one-step transition distribution; the proposed estimation procedure is a pure-jump counterpart to the Gaussian quasi-maximum likelihood estimation. Under some regularity conditions, we will show the asymptotic mixed normality of the proposed estimator, revealing that the proposed estimator is asymptotically much more efficient than the Gaussian quasi-maximum likelihood estimator..
23. Hiroki Masuda, On optimal estimation of stable Ornstein-Uhlenbeck processes, Dynstoch meeting 2013, 2013.04, [URL], Ornstein-Uhlenbeck (OU) processes driven by a Levy process form a particular tractable class of Markovian stochastic differential equations with jumps. Among them, the non-Gaussian stable driven ones, the study of which dates back to Doob's work in 1942, are known to have a pretty inherent character. Especially, a special property of stable integrals allows us to exactly generate the discrete-time sample from the process, and more importantly, to study in a transparent way the likelihood ratio associated with discrete-time sampling. We are concerned with optimal estimation of the stable OU processes observed at high-frequency. We clarify that, due to the infinite-variance character of the model, the likelihood ratio exhibits entirely different asymptotic behaviors according to whether or not the terminal sampling time tends to infinity. When the terminal time is a fixed time, we present the LAMN (Local Asymptotic Mixed Normality) structure of the statistical model, entailing the notion of asymptotic efficiency of a regular estimator. Also presented is how to construct some simple rate-efficient estimators having asymptotic mixed normality, together with numerical experiments..
24. 増田 弘毅, 安定Ornstein-Uhlenbeck過程の推定について, ASC2013 Asymptotic Statistics and Computations , 2013.03, [URL], 非正規安定Ornstein-Uhlenbeck過程から固定期間高頻度観測が得られる状況において,ドリフトパラメータに関する統計的実験列の局所漸近混合正規性を示す.
当該モデルは離散時間AR(1)モデルの連続時間版に相当するが,自己回帰係数の符号に制約がなく,従って, 特に単位根問題が現れないことになる.
これは信頼区間や予測モデルの構成が統一的に行えることを意味する.簡易的な最適推定量の構成に付いても触れる..
25. 増田 弘毅, Levy積分の条件付き期待値の数値計算へ向けて, ASC2013 Asymptotic Statistics and Computations , 2013.03, [URL], Levy積分および多重Levy積分に関する条件付き期待値の公式を提示し,その数値計算方法について議論する.
当該公式は無限分解可能分布 の特性関数で表現され,Wiener積分の場合に知られている既存の公式の拡張版に相当する.Levy汎関数の期待値の近似公式への応用に言及する..
26. 増田 弘毅, 確率微分方程式の自己正規化残差について, 日本数学会 秋季総合分科会, 2012.09, [URL], 固定観測期間上で, 一種の確率微分方程式から高頻度データが得られる統計モデルを考える.
オイラー近似に基づく近似的な自己正規化残差を導入し, それを元に構成される$k$次標本積率の漸近挙動を明らかにする.
応用例として, 標本歪度と標本尖度に基づくJarque-Bera (JB) 型の統計量を構成し, ジャンプ部分を有するか否かの検定問題へ適用する;
微調整パラメータが不要な検定方式なので, 実用性が高い. 更に, i.i.d.モデルや離散時間時系列モデルとの顕著な違いとして,
標本歪度のみで漸近的にあらゆるジャンプ要素を検出可能 (ノイズ過程の任意の非正規性に対する検定の一致性に相当) であることを示す..
27. 増田 弘毅, 自己正規化残差系列の漸近挙動, 統計関連学会連合大会, 2012.09, [URL], 固定観測期間上で, 一種の確率微分方程式から高頻度データが得られる統計モデルにおいて近似的な自己正規化残差を導入し, それを元に構成される$k$次標本積率の漸近挙動を明らかにする.
応用例として, 標本歪度と標本尖度に基づくJarque-Bera (JB) 型の統計量を構成し, ジャンプ部分を有するか否かの検定問題へ適用する; 微調整パラメータが不要な検定方式なので, 実用性が高い.
更に, i.i.d.モデルや離散時間時系列モデルとの顕著な違いとして, 標本歪度のみで漸近的にあらゆるジャンプ要素を検出可能 (ノイズ過程の任意の非正規性に対する検定の一致性に相当) であることに言及する..
28. 増田 弘毅, 確率過程における推測問題と残差系列 etc., 統計サマーセミナー, 2012.08, [URL], レヴィ過程で摂動されるセミパラメトリックな微分方程式モデルの係数の推定を考える際には,
ノイズの確率構造や係数関数の誤特定に伴って通常の疑似最尤推定量の漸近挙動(収束速度,漸近分布の構造)が変わることが知られている.
本講演では,特に一種の残差系列から成る汎関数の漸近挙動を紹介し,その適合度検定への応用を紹介する..
29. Hiroki Masuda, Non-Gaussian quasi-likelihoods for estimating jump SDE, 8th World Congress in Probability and Statistics, 2012.07, [URL], We consider a stochastic differential equation driven by a stable-like Levy process, which is observed at high frequency.
In this talk, we will introduce a quasi-maximum likelihood estimator based on the local-stable approximation of the transition laws.
This is a pure-jump counterpart to the local-Gauss contrast function, well-suited for the case of diffusions.
Under some regularity conditions, we will present asymptotic distribution results, which is entirely different from the Gaussian quasi-likelihood case and much more efficient.
In particular, the rate of convergence of the estimator obtained is much better
and they are jointly asymptotically normal and mixed-normal according as the terminal sampling tends to infinity or not. .
30. Hiroki Masuda, Non-Gaussian quasi likelihood in estimating jump SDE, 2nd Asian Pacific Rim Meeting, 2012.07, [URL], 非正規安定レヴィ過程で微小時間近似できる確率微分方程式モデルの推定問題を考察した.当該モデルでは従来の正規型擬似最尤推定は効率が悪いことが知られており,新たな推定手法が要求される.筆者は,データ増分の非正規安定近似を介した新しい擬似尤度推定法を考案し,その漸近挙動を導出した.特に,ドリフト推定量の有界時間区間上での漸近混合正規性,および推定量の収束率の改善など,正規型では決して得られない(好ましい)現象が明らかとなった..
31. Hiroki Masuda, Local-stable contrast function, Dynstoch meeting 2012, 2012.06, [URL], We consider a stochastic differential equation driven by a stable-like Levy process, which is observed at high frequency.
In this talk, we will introduce a quasi-maximum likelihood estimator based on the local-stable approximation of the transition laws.
This is a pure-jump counterpart to the local-Gauss contrast function, well-suited for the case of diffusions.
Under some regularity conditions, we will present asymptotic distribution results, which is entirely different from the Gaussian quasi-likelihood case and much more efficient.
In particular, the rate of convergence of the estimator obtained is much better
and they are jointly asymptotically normal and mixed-normal according as the terminal sampling tends to infinity or not.
.
32. 増田 弘毅, 確率過程モデルの自己正規化残差について, 応用統計学会, 2012.05, 固定観測期間上で, 一種の確率微分方程式から高頻度データが得られる統計モデルを考える.
モデルの背景を概観した後, オイラー近似に基づく近似的な自己正規化残差を導入し, それを元に構成される$k$次標本積率の漸近挙動を明らかにする.
特に, 標本歪度と標本尖度に基づくJarque-Bera型の統計量を構成して駆動ノイズ過程の分布に関する検定問題へ適用する. これはモデルがジャンプ部分を有するか否かの検定に相当し,
拡散過程 (ジャンプがない) が背後に走っているという帰無仮説のための実用性の高い検定方式を与える.
i.i.d.モデルや時系列モデルとの顕著な違いとして, 標本歪度のみで漸近的にあらゆるジャンプ要素を検出可能という意味での検定の一致性が得られることを示す..
33. 増田弘毅, Asymptotic mixed normality in estimation of jump SDE, Statistics for Stochastic Processes: Inference, Limit Theorems, Finance and Data Analysis, 2012.03, [URL], We introduce some quasi-likelihood approach for estimating a class of stochastic differential equations (SDE) driven by a pure-jump Levy process. Under an infill-sampling scheme, we present the asymptotic mixed normality of the proposed..
34. 増田弘毅, Very simple estimation of a non-Gaussian process model, Forum "Math-for-Industry" 2011, 2011.10, [URL], Modelling and estimation of time-varying phenomena over continuous time is an important subject in many application fields such as signal processing, mathematical finance, and so on. On the one hand, a classical and conventional way is to model on the basis of a Wiener process, that is, the Gaussian process with independent and stationary increments. As is well-known, its mathematically beautiful nature has led to a vast amount of literature on stochastic and statistical analyses of Wiener-driven models, such as diffusions and, more generally, continuous Ito semimartingales. On the other hand, nevertheless, the Gaussianity is actually recognized to be insufficient or inappropriate in some fields; for instance, one often needs to accommodate jumps and heavier-tailed transition probability in the process in question. Non-Gaussian processes can form a rich class of statistical models, even in the framework of Levy processes (the continuous-time random walk) including Wiener and Poisson processes as special cases. Within a class of non-Gaussian processes driven by a stable Levy process and observed at high-frequency, we will provide a pretty practical estimation procedure with a rigorous asymptotic distributional result. Through simulation experiments, our estimators turned out to have rather reliable performance..
35. Hiroki Masuda, On quasi-likelihood analyses for stochastic differential equations with jumps, The International Statistical Institute (ISI) Meeting 2011 Dublin, 2011.08, [URL], ジャンプを持つ一般の確率微分方程式モデルについて,高頻度離散観測に基づいた統計的漸近推測を考える.ここでは尤度関数が陽に求まらず,通常の尤度解析の直接適用は実用上不可能であるため,実用性の高い別の推定手法が必要となる.本講演では先ず,典型的な正規型疑似尤度推定量(GQMLE)について,ジャンプを持つ当該モデルにおいては,漸近正規性を有するものの期待される最適収束率を達成できないことを示す.次にその事実を踏まえ,より収束率および漸近効率の高い非正規型疑似尤度に基づく新しい推定量(NGQMLE)を構築し,その漸近挙動を明らかにする.更に数値実験例を通じて,提案したNGQMLEがGQMLEを優越する推定精度を呈することを示す..
36. Hiroki Masuda, On self-normalized residuals of SDE, Dynstoch meeting 2011, 2011.06, [URL].
37. Hiroki Masuda, Cauchy quasi-likelihood in SDE estimation, Asymptotical Statistics of Stochastic Processes VIII, 2011.03, [URL].
38. Hiroki Masuda, Non-Gaussian quasi-likelihood estimation of jump processes, CREST and Sakigake International Symposium Asymptotic Statistics, Risk and Computation in Finance and Insurance 2010, 2010.12, [URL].
学会活動
所属学会名
日本統計学会
日本数学会
学会誌・雑誌・著書の編集への参加状況
2019.01, Bernoulli journal, 国際, 編集委員.
2014.01~2020.01, Statistical Inference for Stochastic Processes , 国際, 編集委員.
2013.06~2017.05, Journal of the Japan Statistical Society, 国際, 編集委員.
学術論文等の審査
年度 外国語雑誌査読論文数 日本語雑誌査読論文数 国際会議録査読論文数 国内会議録査読論文数 合計
2018年度 10  10 
2017年度 11  11 
2016年度 10  10 
2015年度 11  11 
2014年度      
2013年度    
2012年度    
2011年度      
2010年度      
2009年度      
2008年度    
2007年度      
2006年度      
2005年度    
2004年度      
2003年度      
その他の研究活動
海外渡航状況, 海外での教育研究歴
Technical University of Delft, Holland, 2019.06~2019.06.
SAPIENZA University of Rome, Italy, 2019.03~2019.03.
University of Copenhagen, Denmark, 2019.03~2019.03.
University of Pisa, Italy, 2018.12~2018.12.
National University of Singapore, Singapore, 2018.06~2018.06.
Dynstoch meeting, Portugal, 2018.06~2018.06.
University of Milan, Italy, 2018.03~2018.03.
University of London, UnitedKingdom, 2017.12~2017.12.
Hotel "New Peterhof", Russia, 2017.07~2017.07.
Hong Kong University of Sciences and Technology, China, 2017.06~2017.06.
University of Siegen, Germany, 2017.04~2017.04.
University of Seville, Spain, 2016.12~2016.12.
University of Maine, France, 2016.09~2016.09.
The Fields Institute,University of Toronto, Canada, 2016.06~2016.06.
The Chinese University of Hong Kong, China, 2016.06~2016.06.
University Rennes 2, France, 2016.06~2016.06.
University Pierre and Marie Curie, France, 2016.03~2016.03.
National University of Singapore, Singapore, 2015.12~2015.12.
Riocentro, Brazil, 2015.07~2015.07.
University of Lund, Sweden, 2015.05~2015.05.
University of Maine, France, 2015.03~2015.03.
University of Pisa, Italy, 2014.12~2014.12.
Howard International House, Taiwan, 2014.07~2014.07.
Senate House, University of London, UnitedKingdom, 2013.12~2013.12.
Hong Kong Convention and Exhibition Centre, China, 2013.08~2013.08.
Eotvos Lorand University, Hungary, 2013.07~2013.07.
University of Copenhagen, Denmark, 2013.04~2013.04.
Grand Cevahir Hotel & Convention Center, Turkey, 2012.07~2012.07.
Institut Henri Poincare, France, 2012.06~2012.06.
Institut Louis Bachelier, France, 2012.03~2012.03.
University of Hawaii, UnitedStatesofAmerica, 2011.10~2011.10.
The Convention Centre Dublin, Ireland, 2011.08~2011.08.
University of Heiderberg, Germany, 2011.06~2011.06.
University of Maine, France, 2011.02~2011.02.
University of Florence, Italy, 2011.02~2011.02.
University of Piraeus, Greece, 2010.08~2010.08.
University of Angers, France, 2010.06~2010.06.
Department of Mathematical Stochastics, University of Freiburg, Germany, 2010.02~2010.02.
Humboldt University of Berlin, Germany, 2009.10~2009.10.
University of Milan, Italy, 2009.07~2009.07.
University of Maine, France, 2009.03~2009.03.
University of Padova, Italy, 2008.06~2008.06.
Seoul National University, Korea, 2008.03~2008.03.
University of Maine, France, 2007.03~2007.03.
Seoul National University, Korea, 2006.12~2006.12.
University Paris 10, France, 2006.11~2006.12.
Moscow State University, Russia, 2006.09~2006.09.
University of Mainz, Germany, 2006.06~2006.06.
University of La Rochelle, France, 2005.10~2005.10.
University of Maine, France, 2005.01~2005.01.
Seoul National University, Korea, 2004.11~2004.11.
University of Copenhagen, Denmark, 2004.06~2004.06.
外国人研究者等の受入れ状況
2016.05~2016.05, 2週間未満, Institute of Mathematics of NAS of Ukraine, Japan.
受賞
日本統計学会研究業績賞, 日本統計学会, 2014.09.
小川研究奨励賞受賞者, 日本統計学会, 2006.09.
研究資金
科学研究費補助金の採択状況(文部科学省、日本学術振興会)
2017年度~2019年度, 基盤研究(C), 代表, 非正規型疑似尤度解析による確率過程推測の深化.
2014年度~2016年度, 基盤研究(C), 代表, 疑似安定過程モデルによる新たな各区率過程推測論の基盤構築とその実装.
2011年度~2013年度, 若手研究(B), 代表, ジャンプ過程に対する統計的漸近推測理論の構築とその応用.
2008年度~2010年度, 若手研究(B), 代表, 確率過程に対する統計的漸近推測の理論構築とその高頻度データ解析への応用.
2005年度~2007年度, 若手研究(B), 代表, 無限分解可能過程からの離散観測に基づく未知母数の推定および関連した高次理論.

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