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Boundary-crossing probabilities of some random fields related to likelihood ratio tests for epidemic alternatives

Part of: Parametric inference Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Qiwei Yao
Qiwei Yao*
Affiliation:
Southeast University, Nanjing
*
∗ Present address: Institute of Mathematics and Statistics, University of Kent, Canterbury, Kent CT2 7NF, UK.
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Abstract

We consider the likelihood ratio tests to detect an epidemic alternative in the following two cases of normal observations: (1) the alternative specifies a square wave drift in the mean value of an i.i.d. sequence; (2) the alternative permits a square wave drift in the intercept of a simple linear regression model. To develop the approximations for the significance levels leads us to consider boundary-crossing problems of some two-dimensional discrete-time Gaussian fields. By the method which was proposed originally by Woodroofe (1976) and adapted to study maxima of some random fields by Siegmund (1988), some large deviations for the conditional non-linear boundary-crossing probabilities are developed. Some results of Monte Carlo experiments confirm the accuracy of these approximations.

Keywords

LARGE DEVIATIONGAUSSIAN FIELDS

MSC classification

Primary: 60F10: Large deviations
Secondary: 60G15: Gaussian processes 62F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 52 - 65
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research supported partially by the Alexander von Humboldt-Stiftung, the National Science Foundation of China, and the Deutsche Forschungsgemeinschaft.

References

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