第32回研究会

開催日：

2018年10月3日 (水)　18:00-19:00

会場：

丸の内永楽ビルディング18階 首都大学東京 丸の内サテライトキャンパス

報告者：

Prof. Fumiya Akashi (Waseda University, Research Institute for Science and Engineering)

タイトル：

Robust statistical inference for nonstandard time series models and related topics

概要Abstract

This talk develops robust statistical inference procedures for various nonstandard time series models. In the context of time series analysis, statistical treatment of heavy tails and long-range dependence has attracted much attention. The problems brought by such nonstandard aspects often appear. For example, the rate of convergence of fundamental statistics contains unknown tail/Hurst index, and the limit distributions of classical statistics become intractable. As a result, it is infeasible to determine cut-off points for confidence intervals or critical values for test statistics in practice. To overcome such hurdles, we employee the least absolute deviations regression, self-normalization and self-weighting methods, and construct the robust inference procedures in the following three topics:
(1) The first part of this talk considers robust interval estimation for time series regression models whose innovation and covariate processes have possibly heavy-tails and/or long-range dependence. To make inference for such model, we introduce the self-normalized subsampling method following Akashi et al. (J. Time Ser. Anal. 39:417-432, 2018). As a result, we can construct confidence region for the regression parameter of the model without knowledge of tail/Hurst-indices of the underlying process.
(2) The second part of this talk introduces the self-weighted generalized empirical likelihood (GEL) statistic proposed by Akashi (Stat. Inference Stoch. Process 20(3):291-313, 2017) and its application to a change point detection problem (Akashi et al. (J. Time Ser. Anal. DOI: 10.1111/jtsa.12405, 2018)). The self-weighting method introduced by Ling (2005) enables us to construct a robust test statistic whose limit distribution is pivotal, regardless of whether the model has finite variance of not. We extend Ling (2005)’s method to the GEL statistics and elucidate the limit distribution of the proposed statistic. Some simulation experiments illustrate the desirable properties of the proposed method in practical situations.
(3) The third part of this talk provides a robust inference procedure in directional data analysis. We first review the recent development in directional statistics, and second introduce new robust inference method for circular-linear regression models. Since the extension of the methodologies in the “linear” statistics to the “circular” statistics is not trivial, the proposed method includes a lot of novel aspects.

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