The problem of nonnegative quadratic estimation of a parametric function #( ;, _)=;$F;Necessary and sufficient conditions are given for y$A 0 y to be a minimum biased estimator for #. It is shown how to formulate the problem of finding a nonnegative minimium biased estimator of # as a conic optimization problem, which can be efficiently solved using convex optimization techniques. Models with two variance components are considered in detail. Some applications to one-way classification mixed models are given. For these models minimum biased estimators with minimum norms for square of expectation ; 2 and for _ 2 1 are presented in explicit forms.
Elsevier ScienceAMS 1991 subject classifications: 62J05; 62H12; 90C25.
In the paper, the problem of the existence of the maximum likelihood estimate and the REML estimate in the variance components model is considered. Errors in the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhyā 61, 1999), giving a necessary and sufficient condition for the existence of the maximum likelihood estimate in this model, are pointed out and corrected. A new proof of Theorem 3.4 in the Demidenko and Massam's article, concerning the existence of the REML estimate of variance components, is presented.
Nonparametric density estimation methods have been used for precipitation estimation for decades. The new approach for estimating the density proposed recently by Geenens and Wang appears to offer advantages over them as far as their behavior in the tail is concerned. Real data analyses presented in this paper confirm the usefulness of this new approach for precipitation modelling.
We extend the results concerning the upper bounds for the maximum likelihood degree and the REML degree of the one-way random effects model presented in Gross et al. [Electron. J. Stat. 6 (2012), pp. 993-1016] to the case of the normal linear mixed model with two variance components. Then we prove that both parts of Conjecture 1 in the paper of Gross et al., which concerns a certain extension of the one-way random effects model, are true under fairly mild conditions.
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