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Hiroki Masuda Last modified date:2019.02.05



Graduate School


Homepage
http://www2.math.kyushu-u.ac.jp/~hiroki/hmhp.html
Presonal homepage .
Academic Degree
PhD. (Mathematical Sciences)
Country of degree conferring institution (Overseas)
No
Field of Specialization
Mathematical statistics, stochastic process model
ORCID(Open Researcher and Contributor ID)
0000-0002-5553-9201
Total Priod of education and research career in the foreign country
00years00months
Outline Activities
My researches concern asymptotic statistical inference for stochastic processes, especially, of Levy driven models with/without jumps. I have interest in: asymptotic distributional theory of various statistics; higher order approximation of statistical functionals; and development of how to compute complicated conditional expectations not admitting explicit analytical expressions. Also examined is derivation of the mixing property and its rate of stochastic processes, which is essential when considering ergodic models. Also, I am interested in application of the local non-Gaussian stable approximation to statistics. Also investigated is to implement the methodologies thus obtained in the statistical software, and further to apply them to several areas such as sciences and industry.
Research
Research Interests
  • Development of theory of statistical inference for stochastic processes, and its implementation
    keyword : Asymptotic statistics, Stochastic process, Large and high-frequency dependent data analysis
    2000.04Statistical inference for stochastic processes, distributional theory for statistical functionals.
Academic Activities
Reports
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.
Papers
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, 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, 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. 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, 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..
4. Hiroki Masuda, Parametric estimation of Levy processes, Levy Matters IV, Estimation for Discretely Observed Levy Processes, 10.1007/978-3-319-12373-8_3, 2128, 179-286, 2014.12, The main purpose of this chapter is to present some theoretical aspects of parametric estimation of Levy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of explicit estimating functions are discussed. In addition to the asymptotic normality at several rates of convergence, a uniform tail-probability estimate for statistical random fields is given.As specific cases, we discuss method of moments for the stable Levy processes in much greater detail, with briefly mentioning locally stable Levy processes too. Also discussed is, due to its theoretical importance, a brief review of how the classical likelihood approach works or does not, beyond the fact that the likelihood function is not explicit..
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, 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.
9. Hiroki Masuda, Ergodicity and exponential $\beta$-mixing bound for multidimensional diffusions with jumps, Stochastic Processes and their Applications, 117, 35-56, 2007.01.
10. 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.
11. 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.
12. Hiroki Masuda, Classical method of moments for partially and discretely observed ergodic models, Statistical Inference for Stochastic Processes, 8, no.1, 25-50., 2005.01.
13. Hiroki Masuda, On multidimensional Ornstein-Uhlenbeck processes driven by a general Lévy process, Bernoulli, 10. no.1, 1-24., 2004.01.
Presentations
1. Alexandre Brouste, Hiroki Masuda, Efficient estimation of stable Lévy process, ASC2018, Asymptotic Statistics and Computations, 2018.02.
2. 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..
3. Hiroki Masuda, Stable quasi-likelihood regression, EcoSta 2017, 2017.06.
4. Hiroki Masuda, Shoichi Eguchi, Yuma Uehara, Lévy SDE inference in Yuima package, Dynstoch meeting 2017, 2017.04.
5. Hiroki Masuda, Locally stable regression without ergodicity and finite moments, Hokkaido International Symposium "Recent Developments of Statistical Theory in Statistical Science", 2016.10.
6. 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..
7. Hiroki Masuda, On Asymptotics of multivariate non-Gaussian quasi-likelihood, The 4th Institute of Mathematical Statistics Asia Pacific Rim Meeting, 2016.06.
8. Hiroki Masuda, Lévy in quasi-likelihood estimation of SDE, Statistics for Stochastic Processes and Analysis of High Frequency Data V, 2016.03, 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..
9. 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..
10. Hiroki Masuda, On variants of stable quasi-likelihood for Levy driven SDE, Statistique Asymptotique des Processus Stochastiques X, 2015.03.
11. Hiroki Masuda, On sampling problem for pure-jump SDE , 3rd APRM, Taipei, 2014.07.
12. 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..
13. 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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14. Osaka University, [URL].
15. 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..
16. 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..
17. 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..
18. Hiroki Masuda, Non-Gaussian quasi-likelihoods for estimating jump SDE, 8th World Congress in Probability and Statistics, 2012.07, 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. .
19. Hiroki Masuda, Non-Gaussian quasi likelihood in estimating jump SDE, 2nd Asian Pacific Rim Meeting, 2012.07, 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..
20. Hiroki Masuda, Local-stable contrast function, Dynstoch meeting 2012, 2012.06, 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.
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Awards
  • Studies in statistical inference for stochastic processes with jumps and their implementation
  • Simple estimators for parametric Markovian trend of ergodic processes based on sampled data
Educational
Educational Activities
Lectures: Mainly, (i) elementary mathematical statistics, and (ii) statistical tools for data analyses.
Exercise classes: (i) metric and topological spaces; (ii) statistics; (iii) exploratory mathematics; and (iv) Lebesgue integration theory.