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The Encompassing Principle and Hypothesis Testing

Published online by Cambridge University Press:  11 February 2009

Maozu Lu  and
Grayham E. Mizon
Maozu Lu
Affiliation:
University of Southampton
Grayham E. Mizon
Affiliation:
University of Southampton and European University Institute
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Abstract

The exponentially tilted family of densities is used to discuss the relationship between the encompassing principle and the M-test or conditional moment testing principle. It is shown that the two principles are capable of generating the same test statistics and in this sense equivalent. However, there are differences in motivation and emphasis underlying the principles that are important in econometric modeling. In addition, parsimonious encompassing interpretations for test statistics, including those of Cox (1961, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability I, pp. 105-123; 1962, Journal of the Royal Statistical Society, Series B 24, 406-424) and Atkinson (1970, Journal of the Royal Statistical Society, Series B 32, 323-344) are provided.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 5 , December 1996 , pp. 845 - 858
Copyright
Copyright © Cambridge University Press 1996

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