Likelihood Inferencein the Errors - in - Variables Modelby
نویسندگان
چکیده
We consider estimation and conndence regions for the parameters and based on the observations is known up to a constant. We study the asymptotic performance of the estimators deened as the maximum likelihood estimator under the assumption that Z 1 ; : : :; Z n is a random sample from a completely unknown distribution. These estimators are shown to be asymptotically eecient in the semi-parametric sense if this assumption is valid. These estimators are shown to be asymptotically normal even in the case that Z 1 ; Z 2 ; : : : are arbitrary constants satisfying a moment condition. Similarly we study the conndence regions obtained from the likelihood ratio statistic for the mixture model and show that these are asymptotically consistent both in the mixture case and in the case that Z 1 ; Z 2 ; : : : are arbitrary constants.
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