Geometric understanding of likelihood ratio statistics

Jianqing Fan*, Wing Hung Wong, Hui-Nien Hung


研究成果: Article同行評審

15 引文 斯高帕斯(Scopus)


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.

頁(從 - 到)836-841
期刊Journal of the American Statistical Association
出版狀態Published - 1 9月 2000


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