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A simultaneous test in the presence of nested alternative hypotheses

Published online by Cambridge University Press:  14 July 2016

Yuzo Hosoya
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Abstract

This paper considers the generalized likelihood ratio (GLR) test or its modification dealing with nested models. The algorithm for evaluating the critical values and the error-rates for the canonical tests are provided; a table of critical values of a class of GLR tests is also given. The test proposed in the paper has applications in time-series model selection.

Keywords

HYPOTHESIS TESTINGTIME-SERIES ANALYSISLIKELIHOOD RATIO TESTASYMPTOTIC THEORYNUMERICAL INTEGRATIONNESTED MODELSMODEL SELECTION
Type
Part 3—Hypothesis Testing and Distribution Theory for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 187 - 200
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Chernoff, H. (1954) On the distribution of the likelihood ratio. Ann. Math. Statist. 25, 573–578.CrossRefGoogle Scholar
Cox, D. R. (1961) Tests of separate families of hypotheses. Proc. 4th. Berkeley Symp. Math. Statist. Prob. 1, 105–123.Google Scholar
Dunsmuir, W. and Hannan, E. J. (1976) Vector linear time-series models. Adv. Appl. Prob. 8, 334–364.Google Scholar
Hosoya, Y. (1984) Information criteria and tests for time-series models. In Time Series Analysis: Theory and Practice 5, ed. Anderson, O. D., Elsevier, Amsterdam.Google Scholar
Hosoya, Y. and Taniguchi, M. (1982) A central limit theorem for stationary processes and the parameter estimation of linear processes. Ann. Statist. 10, 132–153.Google Scholar
Stone, M. (1969) The role of significance testing: some data with a message. Biometrika 56, 485–493.Google Scholar
Wald, A. (1943) Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Amer. Math. Soc. 54, 426–482.CrossRefGoogle Scholar