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 |
|---|---|
| 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 |
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Keywords
- 60F10
- 62F03
- 62M10
- Bahadur efficiency
- Gaussian stationary process
- Hypothesis testing
- Large deviation
- Spectral density
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability
Cite this
On large deviation asymptotics of some tests in time series. / Taniguchi, Masanobu.
In: Journal of Statistical Planning and Inference, Vol. 97, No. 1, 01.08.2001, p. 191-200.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On large deviation asymptotics of some tests in time series
AU - Taniguchi, Masanobu
PY - 2001/8/1
Y1 - 2001/8/1
N2 - 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.
AB - 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.
KW - 60F10
KW - 62F03
KW - 62M10
KW - Bahadur efficiency
KW - Gaussian stationary process
KW - Hypothesis testing
KW - Large deviation
KW - Spectral density
UR - http://www.scopus.com/inward/record.url?scp=0041401243&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0041401243&partnerID=8YFLogxK
U2 - 10.1016/S0378-3758(00)00353-0
DO - 10.1016/S0378-3758(00)00353-0
M3 - Article
VL - 97
SP - 191
EP - 200
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
IS - 1
ER -