Title of article :
Asymptotics for likelihood ratio tests under loss of identifiability.
Author/Authors :
Liu، Xin نويسنده , , Shao، Yongzhao نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2003
Pages :
-806
From page :
807
To page :
0
Abstract :
This paper describes the large sample properties of the likelihood ratio test statistic (LRTS) when the parameters characterizing the true null distribution are not unique. It is well known that the classical asymptotic theory for the likelihood ratio test does not apply to such problems and the LRTS may not have the typical chi-squared type limiting distribution. This paper establishes a general quadratic approximation of the log-likelihood ratio function in a Hellinger neighborhood of the true density which is valid with or without loss of identifiability of the true distribution. Under suitable conditions, the asymptotic null distribution of the LRTS under loss of identifiability can be obtained by maximizing the quadratic form. These results extend the work of Chernoff and Le Cam. In particular, applications to testing the number of mixture components in finite mixture models are discussed.
Keywords :
Donsker class , Hellinger distance , Likelihood ratio test , loss of identifiability , finite mixture model
Journal title :
Annals of Statistics
Serial Year :
2003
Journal title :
Annals of Statistics
Record number :
74509
Link To Document :
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