Bahadur, R. R.
(1972)
*Examples of inconsistency of the likelihood ratio statistic*
Sankhya, 34
(1).
pp. 81-84.
ISSN 0972-7671

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## Abstract

In testing a null hypothesis on the basis of independent and identically distributed observations let T^{ˆ}_{n} be the normalized likelihood ratio statistic and let L^{ˆ}_{n} be the level attained by T^{ˆ}_{n} when the sample size is n. It is known (cf. Bahadur (1965)) that in typical cases T^{ˆ}_{n}→J and n^{-1}log L^{ˆ}_{n}→-J as n→∞, where J is a positive constant defined in terms of the Kullback-Leibler information numbers. This note gives examples where these properties of likelihood ratios do not hold; in some example L^{ˆ}_{n} does not even tend to zero. The examples show that some of the regularity assumptions of Bahadur (1965) are essential in the general case.

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ID Code: | 27040 |

Deposited On: | 08 Dec 2010 12:48 |

Last Modified: | 11 May 2011 04:26 |

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