On the Asymptotic Performance of the Log Likelihood Ratio Statistic for the Mixture Model and Related Results I
نویسندگان
چکیده
The classical distribution theory of the log likelihood ratio test statistic does not hold for testing homogeneity (i.e., no mixture) against mixture alternatives. Asymptotic theory for this problem is developed. For some special cases, asymptotically locally minimax tests are also found. It is pointed out that the main problem is lack of identifiability of the usual parameterization even when the mixtures are identifiable; if one chooses an identifiable parameterisation, then there is a problem of differentiability of the density.
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