Exponential Approximation of the Likelihood Functions and Hypotheses Testing in the Independent Not Identically Distributed Case
Titel:
Exponential Approximation of the Likelihood Functions and Hypotheses Testing in the Independent Not Identically Distributed Case
Auteur:
Philippou, Andreas N.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 2 (1973) nr. 5 pagina's 401-418
Jaar:
1973
Inhoud:
Let θ be an open subset of Rk, k ≥ 1, and for each θεθ let X1, …, Xn be independent but not necessarily identically distributed random variables defined on the probability space .Under a set of non-standard conditions (that is, not Cramer-type), the likelihood function is approximated by an exponential family of probability density functions, and the statistical implications of this result to hypotheses testing problems are indicated. In addition, sufficient conditions for the assumptions to hold are also given, and their applicability is illustrated by means of a simple example.
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