Hellinger distance estimation for nonregular spectra
Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 1, pp. 188-200
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For Gaussian stationary processes, a time series Hellinger distance $T(f,g)$ for spectra $f$ and $g$ is derived. Evaluating $T(f_\theta,f_{\theta+h})$ of the
form $O(h^\alpha)$, we give $1/\alpha$-consistent asymptotics of the maximum
likelihood estimator of $\theta$ for nonregular spectra. For regular spectra,
we introduce the minimum Hellinger distance estimator
$\widehat{\theta}=\operatorname{arg}\min_\theta T(f_\theta,\widehat{g}_n)$,
where $\widehat{g}_n$ is a nonparametric spectral density estimator. We show
that $\widehat\theta$ is asymptotically efficient and more robust than the
Whittle estimator. Brief numerical studies are provided.
Keywords:
Gaussian stationary process, Hellinger distance estimator, nonregular spectra, asymptotically efficient, robust.
@article{TVP_2024_69_1_a9,
author = {M. Taniguchi and Y. Xue},
title = {Hellinger distance estimation for nonregular spectra},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {188--200},
publisher = {mathdoc},
volume = {69},
number = {1},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2024_69_1_a9/}
}
M. Taniguchi; Y. Xue. Hellinger distance estimation for nonregular spectra. Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 1, pp. 188-200. http://geodesic.mathdoc.fr/item/TVP_2024_69_1_a9/