## Seminar on Probability and Statistics

Seminar information archive ～09/27｜Next seminar｜Future seminars 09/28～

Organizer(s) | Nakahiro Yoshida, Teppei Ogihara, Yuta Koike |
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**Seminar information archive**

### 2012/10/18

15:15-16:25 Room #006 (Graduate School of Math. Sci. Bldg.)

Quasi-Bayesian analysis of nonparametric instrumental variables models (JAPANESE)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/08.html

**KATO, Kengo**(Department of Mathematics, Graduate School of Science, Hiroshima University)Quasi-Bayesian analysis of nonparametric instrumental variables models (JAPANESE)

[ Abstract ]

This paper aims at developing a quasi-Bayesian analysis

of the nonparametric instrumental variables model, with a focus on the

asymptotic properties of quasi-posterior distributions. In this paper,

instead of assuming a distributional assumption on the data generating

process, we consider a quasi-likelihood induced from the conditional

moment restriction, and put priors on the function-valued parameter.

We call the resulting posterior quasi-posterior, which corresponds to

``Gibbs posterior'' in the literature. Here we shall focus on sieve

priors, which are priors that concentrate on finite dimensional sieve

spaces. The dimension of the sieve space should increase as the sample

size. We derive rates of contraction and a non-parametric Bernstein-von

Mises type result for the quasi-posterior distribution, and rates of

convergence for the quasi-Bayes estimator defined by the posterior

expectation. We show that, with priors suitably chosen, the

quasi-posterior distribution (the quasi-Bayes estimator) attains the

minimax optimal rate of contraction (convergence, respectively). These

results greatly sharpen the previous related work.

[ Reference URL ]This paper aims at developing a quasi-Bayesian analysis

of the nonparametric instrumental variables model, with a focus on the

asymptotic properties of quasi-posterior distributions. In this paper,

instead of assuming a distributional assumption on the data generating

process, we consider a quasi-likelihood induced from the conditional

moment restriction, and put priors on the function-valued parameter.

We call the resulting posterior quasi-posterior, which corresponds to

``Gibbs posterior'' in the literature. Here we shall focus on sieve

priors, which are priors that concentrate on finite dimensional sieve

spaces. The dimension of the sieve space should increase as the sample

size. We derive rates of contraction and a non-parametric Bernstein-von

Mises type result for the quasi-posterior distribution, and rates of

convergence for the quasi-Bayes estimator defined by the posterior

expectation. We show that, with priors suitably chosen, the

quasi-posterior distribution (the quasi-Bayes estimator) attains the

minimax optimal rate of contraction (convergence, respectively). These

results greatly sharpen the previous related work.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/08.html

### 2012/10/05

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

Quasi-likelihood analysis for stochastic regression models from nonsynchronous observations (JAPANESE)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/07.html

**OGIHARA, Teppei**(Center for the Study of Finance and Insurance, Osaka University)Quasi-likelihood analysis for stochastic regression models from nonsynchronous observations (JAPANESE)

[ Abstract ]

高頻度金融時系列データの解析時に, 二資産価格データの共変動を解析する上での問題として

"観測の非同期性"がある. データの線形補完や直前データを用いた補完などによるシンプルな

"同期化"を行ったデータに対する共分散推定量は深刻なバイアスが存在することが知られている.

Hayashi and Yoshida (2005)では, 非同期観測下での共分散のノンパラメトリックな不偏推定量を提案し,

推定量の一致性, 漸近(混合)正規性などを示している.

本発表ではパラメータ付2次元拡散過程の非同期観測の問題に対する, 尤度解析を用いたアプローチを紹介し,

最尤型推定量, ベイズ型推定量の構築とその一致性, 漸近混合正規性に関する結果を紹介する.

[ Reference URL ]高頻度金融時系列データの解析時に, 二資産価格データの共変動を解析する上での問題として

"観測の非同期性"がある. データの線形補完や直前データを用いた補完などによるシンプルな

"同期化"を行ったデータに対する共分散推定量は深刻なバイアスが存在することが知られている.

Hayashi and Yoshida (2005)では, 非同期観測下での共分散のノンパラメトリックな不偏推定量を提案し,

推定量の一致性, 漸近(混合)正規性などを示している.

本発表ではパラメータ付2次元拡散過程の非同期観測の問題に対する, 尤度解析を用いたアプローチを紹介し,

最尤型推定量, ベイズ型推定量の構築とその一致性, 漸近混合正規性に関する結果を紹介する.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/07.html

### 2012/07/27

14:00-17:00 Room #006 (Graduate School of Math. Sci. Bldg.)

General approach to reinforcement learning based on statistical inference (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/06.html

**UENO, Tsuyoshi**(Minato Discrete Structure Manipulation System Project, Japan Science and Technology Agency)General approach to reinforcement learning based on statistical inference (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/06.html

### 2012/05/31

14:50-16:05 Room #006 (Graduate School of Math. Sci. Bldg.)

Holonomic gradient methods for likelihood computation (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/05.html

**SEI, Tomonari**(Department of Mathematics, Keio University)Holonomic gradient methods for likelihood computation (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/05.html

### 2012/05/18

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additive Model (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/04.html

**SUZUKI, Taiji**(University of Tokyo)PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additive Model (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/04.html

### 2012/05/11

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

Efficient Discretization of Stochastic Integrals (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/03.html

**FUKASAWA, Masaaki**(Department of Mathematics, Osaka University)Efficient Discretization of Stochastic Integrals (JAPANESE)

[ Abstract ]

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.

[ Reference URL ]Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/03.html

### 2012/04/27

15:00-16:10 Room #006 (Graduate School of Math. Sci. Bldg.)

Convergence conditions on step sizes in temporal difference learning (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/02.html

**NOMURA, Ryosuke**(Graduate school of Mathematical Sciences, Univ. of Tokyo)Convergence conditions on step sizes in temporal difference learning (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/02.html

### 2012/04/20

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

On the asymptotic mixed normality of the pre-averaged Hayashi-Yoshida

estimator with random and nonsynchronous sampling (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/01.html

**KOIKE, Yuta**(Graduate school of Mathematical Sciences, Univ. of Tokyo)On the asymptotic mixed normality of the pre-averaged Hayashi-Yoshida

estimator with random and nonsynchronous sampling (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/01.html

### 2012/04/13

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

Asymptotic properties of MCMC for cumulative link model (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/00.html

**KAMATANI, Kengo**(Graduate School of Engineering Science, Osaka University)Asymptotic properties of MCMC for cumulative link model (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/00.html

### 2011/11/30

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Information criteria for parametric and semi-parametric models (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/05.html

**HIROSE, Yuichi**(Victoria University of Wellington)Information criteria for parametric and semi-parametric models (JAPANESE)

[ Abstract ]

Since Akaike proposed an Information Criteria, this approach to

model selection has been important part of Statistical data analysis.

Since then many Information Criteria have been proposed and it is still

an active field of research. Despite there are many contributors in this

topic, we have not have proper Information Criteria for semiparametric

models. In this talk, we give ideas to develop an Information Criteria

for semiparametric models.

[ Reference URL ]Since Akaike proposed an Information Criteria, this approach to

model selection has been important part of Statistical data analysis.

Since then many Information Criteria have been proposed and it is still

an active field of research. Despite there are many contributors in this

topic, we have not have proper Information Criteria for semiparametric

models. In this talk, we give ideas to develop an Information Criteria

for semiparametric models.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/05.html

### 2011/10/26

15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)

Statistical models constructed by optimal stationary coupling (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/04.html

**SEI, Tomonari**(Department of Mathematics, Keio University)Statistical models constructed by optimal stationary coupling (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/04.html

### 2011/10/12

15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)

On Convergence Rate of Multiple Kernel Learning with Various Regularization Types (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/03.html

**SUZUKI, Taiji**(University of Tokyo)On Convergence Rate of Multiple Kernel Learning with Various Regularization Types (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/03.html

### 2011/07/13

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Statistical Inference for High-Dimension, Low-Sample-Size Data (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/02.html

**YATA, Kazuyoshi**(Institute of Mathematics, University of Tsukuba)Statistical Inference for High-Dimension, Low-Sample-Size Data (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/02.html

### 2011/06/29

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Statistics in genetic association studies (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/01.html

**OKADA, Yukinori**(Laboratory for Statistical Analysis, Center for Genomic Medicine, RIKEN)Statistics in genetic association studies (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/01.html

### 2011/06/22

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

計算機代数を用いた統計的漸近論 (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/00.html

**KOBAYASHI, Kei**(The Institute of Statistical Mathematics)計算機代数を用いた統計的漸近論 (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/00.html

### 2011/02/02

15:00-16:10 Room #006 (Graduate School of Math. Sci. Bldg.)

An Attempt to formalize Statistical Inferences for Weakly Dependent Time-Series Data and Some Trials for Statistical Analysis of Financial Data (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/08.html

**MIURA, Ryozo**(Hitotsubashi University)An Attempt to formalize Statistical Inferences for Weakly Dependent Time-Series Data and Some Trials for Statistical Analysis of Financial Data (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/08.html

### 2011/01/26

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Semi-parametric profile likelihood estimation and implicitly defined functions (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/07.html

**HIROSE, Yuichi**(Victoria University of Wellington)Semi-parametric profile likelihood estimation and implicitly defined functions (JAPANESE)

[ Abstract ]

The object of talk is the differentiability of implicitly defined functions which we

encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild

(1997, 2001) and Murphy and Vaart (2000) developed methodologies that can avoid dealing with such implicitly

defined functions by reparametrizing parameters in the profile likelihood and using an approximate least

favorable submodel in semi-parametric models. Our result shows applicability of an alternative approach

developed in Hirose (2010) which uses the differentiability of implicitly defined functions.

[ Reference URL ]The object of talk is the differentiability of implicitly defined functions which we

encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild

(1997, 2001) and Murphy and Vaart (2000) developed methodologies that can avoid dealing with such implicitly

defined functions by reparametrizing parameters in the profile likelihood and using an approximate least

favorable submodel in semi-parametric models. Our result shows applicability of an alternative approach

developed in Hirose (2010) which uses the differentiability of implicitly defined functions.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/07.html

### 2011/01/19

15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)

Notes on estimating the probability of ruin and some generalization (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/06.html

**SHIMIZU, Yasutaka**(Osaka University)Notes on estimating the probability of ruin and some generalization (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/06.html

### 2010/10/06

15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)

On multiple kernel learning with elasticnet type regularization (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/05.html

**SUZUKI, Taiji**(University of Tokyo)On multiple kernel learning with elasticnet type regularization (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/05.html

### 2010/07/15

15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)

Mighty convergence in LAD type estimation (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/04.html

**MASUDA, Hiroki**(Graduate School of Mathematics, Kyushu University)Mighty convergence in LAD type estimation (JAPANESE)

[ Abstract ]

We propose a LAD (least absolute deviation) type contrast function for estimating Levy driven Ornstein-Uhlenbeck processes sampled at high frequency. The asymptotic behavior and polynomial-type large deviation inequality concerning the statistical random fields in question are derived, entailing an asymptotic normality and convergence of moments of the LAD estimator. Also, we will mention some numerical experiments done by the R software and some possible extensions of the framework.

[ Reference URL ]We propose a LAD (least absolute deviation) type contrast function for estimating Levy driven Ornstein-Uhlenbeck processes sampled at high frequency. The asymptotic behavior and polynomial-type large deviation inequality concerning the statistical random fields in question are derived, entailing an asymptotic normality and convergence of moments of the LAD estimator. Also, we will mention some numerical experiments done by the R software and some possible extensions of the framework.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/04.html

### 2010/06/09

15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)

Weak convergence of Markov chain Monte Carlo method and its application to Yuima (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/03.html

**KAMATANI, Kengo**(Graduate school of Mathematical Sciences, Univ. of Tokyo)Weak convergence of Markov chain Monte Carlo method and its application to Yuima (JAPANESE)

[ Abstract ]

We examine some asymptotic properties of Markov chain Monte Carlo methods by the weak convergence framework of MCMC. Our purpose is to compare this framework to the Harris recurrence framework. Numerical illustrations will be given via R. The connection to the YUIMA package will also be discussed.

This talk will be held at IT Studio.

[ Reference URL ]We examine some asymptotic properties of Markov chain Monte Carlo methods by the weak convergence framework of MCMC. Our purpose is to compare this framework to the Harris recurrence framework. Numerical illustrations will be given via R. The connection to the YUIMA package will also be discussed.

This talk will be held at IT Studio.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/03.html

### 2010/05/26

16:20-17:30 Room #000 (Graduate School of Math. Sci. Bldg.)

Financial data analysis with R-YUIMA (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/02.html

**FUKASAWA, Masaaki**(CSFI, Osaka Univ.)Financial data analysis with R-YUIMA (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/02.html

### 2010/05/19

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Estimation of the variance-covariance structure for stochastic processes and applications of YUIMA (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/01.html

**YOSHIDA, Nakahiro**(University of Tokyo)Estimation of the variance-covariance structure for stochastic processes and applications of YUIMA (JAPANESE)

[ Abstract ]

We discuss limit theorems and asymptotic expansions in estimation of the variance-covariance structure for Ito processes. We will show some numerical examples by YUIMA, a package for statistical analysis and simulation of stochastic differential equations.

[ Reference URL ]We discuss limit theorems and asymptotic expansions in estimation of the variance-covariance structure for Ito processes. We will show some numerical examples by YUIMA, a package for statistical analysis and simulation of stochastic differential equations.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/01.html

### 2010/04/28

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

A Markov process for circular data (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/00.html

**KATO, Shogo**(The Institute of Statistical Mathematics)A Markov process for circular data (JAPANESE)

[ Abstract ]

We propose a discrete-time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. The proposed model is compared with an existing Markov process for circular data. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered.

[ Reference URL ]We propose a discrete-time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. The proposed model is compared with an existing Markov process for circular data. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/00.html

### 2010/03/29

13:00-14:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Inference for partially observed Markov processes and applications

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/17.html

**Catherine Laredo**(MIA, INRA)Inference for partially observed Markov processes and applications

[ Abstract ]

We present some statistical methods for estimating the param- eters of a population dynamics model of annual plants. It is modelled using multitype branching processes with immigration. The data consist of counts in each type that are measured in several populations for a few consecu- tive years. Parametric inference is first carried out when count data of all types are observed. We prove statistical identifiability for all the parameters ruling the population dynamics model and derive consistent and asymptot- ically Gaussian estimators. However, it often occurs that, in practice, one or more types cannot be observed, leading to partially observed processes. Parametric inference is first studied in the case of Poisson distributions. We characterize the parameter subset where identifiability holds and de- rive consistent and asymptotically normal estimators for this parameter subset. Theses results are then extended to other distributions.

We apply these results to feral oilseed data. The model takes account of reproduction, immigration, and seed survival in a seed bank. The data consist of the number of plants in several developmental stages that were measured in a number of populations for few consecutive years. They are incomplete since seeds could not be counted.

[ Reference URL ]We present some statistical methods for estimating the param- eters of a population dynamics model of annual plants. It is modelled using multitype branching processes with immigration. The data consist of counts in each type that are measured in several populations for a few consecu- tive years. Parametric inference is first carried out when count data of all types are observed. We prove statistical identifiability for all the parameters ruling the population dynamics model and derive consistent and asymptot- ically Gaussian estimators. However, it often occurs that, in practice, one or more types cannot be observed, leading to partially observed processes. Parametric inference is first studied in the case of Poisson distributions. We characterize the parameter subset where identifiability holds and de- rive consistent and asymptotically normal estimators for this parameter subset. Theses results are then extended to other distributions.

We apply these results to feral oilseed data. The model takes account of reproduction, immigration, and seed survival in a seed bank. The data consist of the number of plants in several developmental stages that were measured in a number of populations for few consecutive years. They are incomplete since seeds could not be counted.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/17.html