Weak convergence of marked empirical processes in a hilbert space and its applications

Koji Tsukuda; Yoichi Nishiyama

doi:10.1214/20-ejs1761

Weak convergence of marked empirical processes in a hilbert space and its applications

Koji Tsukuda, Yoichi Nishiyama

School of International Liberal Studies

Research output: Contribution to journal › Article › peer-review

Abstract

We discuss goodness-of-fit tests for stationary ergodic processes based on limit theorems for marked empirical processes viewed as elements of an L² space. Our limit theorems cover a weighted process that enables an Anderson–Darling-type test statistic for the goodness-of-fit tests to be proposed. The procedures presented for these goodness-of-fit tests are novel.

Original language	English
Pages (from-to)	3914-3938
Number of pages	25
Journal	Electronic Journal of Statistics
Volume	14
Issue number	2
DOIs	https://doi.org/10.1214/20-ejs1761
Publication status	Published - 2020

Keywords

Diffusion process
Goodness-of-fit test
Nonlinear time series
Weak convergence in Hilbert space

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/20-ejs1761

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abstract = "We discuss goodness-of-fit tests for stationary ergodic processes based on limit theorems for marked empirical processes viewed as elements of an L2 space. Our limit theorems cover a weighted process that enables an Anderson–Darling-type test statistic for the goodness-of-fit tests to be proposed. The procedures presented for these goodness-of-fit tests are novel.",

keywords = "Diffusion process, Goodness-of-fit test, Nonlinear time series, Weak convergence in Hilbert space",

author = "Koji Tsukuda and Yoichi Nishiyama",

note = "Funding Information: The authors would like to express their sincere gratitude to an associate editor and an anonymous referee who provided us valuable comments. This study was partly supported by Japan Society for the Promotion of Science KAKENHI Grant Number 16H02791 (KT), 18K13454 (KT), 15K00062 (YN), and 18K11203 (YN). This study was mainly carried out when the first author was a member of Graduate School of Arts and Sciences, the University of Tokyo. Publisher Copyright: {\textcopyright} 2020, Institute of Mathematical Statistics. All rights reserved.",

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PY - 2020

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N2 - We discuss goodness-of-fit tests for stationary ergodic processes based on limit theorems for marked empirical processes viewed as elements of an L2 space. Our limit theorems cover a weighted process that enables an Anderson–Darling-type test statistic for the goodness-of-fit tests to be proposed. The procedures presented for these goodness-of-fit tests are novel.

AB - We discuss goodness-of-fit tests for stationary ergodic processes based on limit theorems for marked empirical processes viewed as elements of an L2 space. Our limit theorems cover a weighted process that enables an Anderson–Darling-type test statistic for the goodness-of-fit tests to be proposed. The procedures presented for these goodness-of-fit tests are novel.

KW - Diffusion process

KW - Goodness-of-fit test

KW - Nonlinear time series

KW - Weak convergence in Hilbert space

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Weak convergence of marked empirical processes in a hilbert space and its applications

Abstract

Keywords

ASJC Scopus subject areas

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