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.
Original language | English |
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Pages (from-to) | 191-200 |
Number of pages | 10 |
Journal | Journal of Statistical Planning and Inference |
Volume | 97 |
Issue number | 1 |
DOIs | |
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