On large deviation asymptotics of some tests in time series

Masanobu Taniguchi

doi:10.1016/S0378-3758(00)00353-0

On large deviation asymptotics of some tests in time series

Masanobu Taniguchi

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

1 Citation (Scopus)

Abstract

Let {X_t} be a Gaussian stationary process with spectral density f_θ(λ). The problem considered is that of testing a simple hypothesis H₀:θ=θ₀ against the alternative A:θ≠θ₀. For this we investigate the Bahadur efficiency of the likelihood ratio, Rao, modified Wald and Wald tests. The Bahadur efficiency is based on the large deviation theory. Then it is shown that the asymptotics of the above tests are identical up to second-order in a certain sense. We show that this result makes a sharp contrast with the ordinary higher-order asymptotic theory for tests.

Original language	English
Pages (from-to)	191-200
Number of pages	10
Journal	Journal of Statistical Planning and Inference
Volume	97
Issue number	1
DOIs	https://doi.org/10.1016/S0378-3758(00)00353-0
Publication status	Published - 2001 Aug 1
Externally published	Yes

Keywords

60F10
62F03
62M10
Bahadur efficiency
Gaussian stationary process
Hypothesis testing
Large deviation
Spectral density

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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abstract = "Let {Xt} be a Gaussian stationary process with spectral density fθ(λ). The problem considered is that of testing a simple hypothesis H0:θ=θ0 against the alternative A:θ≠θ0. For this we investigate the Bahadur efficiency of the likelihood ratio, Rao, modified Wald and Wald tests. The Bahadur efficiency is based on the large deviation theory. Then it is shown that the asymptotics of the above tests are identical up to second-order in a certain sense. We show that this result makes a sharp contrast with the ordinary higher-order asymptotic theory for tests.",

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KW - Spectral density

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