@article{76a7cc66b653446493030066c6e08c55,
title = "Weak convergence of marked empirical processes in a hilbert space and its applications",
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.",
year = "2020",
doi = "10.1214/20-ejs1761",
language = "English",
volume = "14",
pages = "3914--3938",
journal = "Electronic Journal of Statistics",
issn = "1935-7524",
publisher = "Institute of Mathematical Statistics",
number = "2",
}