Two-sided tests for change in level for correlated data
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Abstract
The classical problem of change point is considered when the data are assumed to be correlated. The nuisance parameters in the model are the initial level μ and the common variance σ2. The four cases, based on none, one, and both of the parameters are known are considered. Likelihood ratio tests are obtained for testing hypotheses regarding the change in level, δ, in each case. Following Henderson (1986), a Bayesian test is obtained for the two sided alternative. Under the Bayesian set up, a locally most powerful unbiased test is derived for the case μ=0 and σ2=1. The exact null distribution function of the Bayesian test statistic is given an integral representation. Methods to obtain exact and approximate critical values are indicated.
Keywords
Autoregressive Process Bayesian testing Likelihood ratio test Locally most powerful unbiased test Null distributionPreview
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