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Seminar on Probability and Statistics
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Organizer(s) | Nakahiro Yoshida, Teppei Ogihara, Yuta Koike |
|---|
Seminar information archive
2012/10/19
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
SHIMIZU, Yasutaka (Graduate School of Engineering Science, Osaka University)
Asymptotic expansion of ruin probability under Lévy insurance risks (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/09.html
SHIMIZU, Yasutaka (Graduate School of Engineering Science, Osaka University)
Asymptotic expansion of ruin probability under Lévy insurance risks (JAPANESE)
[ Abstract ]
An asymptotic expansion formula of the ultimate ruin probability under L\\'evy insurance risks
is given as the loading factor tends to zero. The formula is obtained via the Edgeworth type expansion of
the compound geometric random sum. We give higher-order expansions of the ruin probability with a certain validity.
This allows us to evaluate quantile of the ruin function, which is nicely applied to estimate the VaR-type risk measure due to ruin.
[ Reference URL ]An asymptotic expansion formula of the ultimate ruin probability under L\\'evy insurance risks
is given as the loading factor tends to zero. The formula is obtained via the Edgeworth type expansion of
the compound geometric random sum. We give higher-order expansions of the ruin probability with a certain validity.
This allows us to evaluate quantile of the ruin function, which is nicely applied to estimate the VaR-type risk measure due to ruin.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/09.html
2012/10/18
15:15-16:25 Room #006 (Graduate School of Math. Sci. Bldg.)
KATO, Kengo (Department of Mathematics, Graduate School of Science, Hiroshima University)
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.)
OGIHARA, Teppei (Center for the Study of Finance and Insurance, Osaka University)
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.)
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
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.)
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
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.)
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
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.)
FUKASAWA, Masaaki (Department of Mathematics, Osaka University)
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.)
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
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.)
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
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.)
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
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.)
HIROSE, Yuichi (Victoria University of Wellington)
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.)
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
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.)
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
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.)
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
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.)
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
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.)
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
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.)
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
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.)
HIROSE, Yuichi (Victoria University of Wellington)
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.)
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
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.)
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
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.)
MASUDA, Hiroki (Graduate School of Mathematics, Kyushu University)
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.)
KAMATANI, Kengo (Graduate school of Mathematical Sciences, Univ. of Tokyo)
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.)
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
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.)
YOSHIDA, Nakahiro (University of Tokyo)
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.)
KATO, Shogo (The Institute of Statistical Mathematics)
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
