標題: Geometric understanding of likelihood ratio statistics
作者: Fan, JQ
Hung, HN
Wong, WH
統計學研究所
Institute of Statistics
公開日期: 1-九月-2000
摘要: It is well known that twice a log-likelihood ratio statistic follows asymptotically a chi-square distribution. The result is usually understood and proved via Taylor's expansions of likelihood functions and by assuming asymptotic normality of maximum likelihood estimators (MLEs). We obtain more general results by using a different approach the Wilks type of results hold as long as likelihood contour sets are fan-shaped. The classical Wilks theorem corresponds to the situations in which the likelihood contour sets are ellipsoidal. This provides a geometric understanding and a useful extension of the likelihood ratio theory. As a result, even if the MLEs are not asymptotically normal, the likelihood ratio statistics can still be asymptotically chi-square distributed. Our technical arguments are simple and easily understood.
URI: http://hdl.handle.net/11536/30259
ISSN: 0162-1459
期刊: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume: 95
Issue: 451
起始頁: 836
結束頁: 841
顯示於類別:期刊論文


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