On ordered normally distributed vector parameter estimates

Abstract : The ordered values of a sample of observations are called the order statistics of the sample and are among the most important functions of a set of random variables in probability and statistics. However the study of ordered estimates seems to have been overlooked in maximum-likelihood estimation. Therefore it is the aim of this communication to give an insight into the relevance of order statistics in maximum-likelihood estimation by providing a second-order statistical prediction of ordered normally distributed estimates. Indeed, this second-order statistical prediction allows to refine the asymptotic performance analysis of the mean square error (MSE) of maximum likelihood estimators (MLEs) of a subset of the parameters. A closer look to the bivariate case highlights the possible impact of estimates ordering on MSE, impact which is not negligible in (very) high resolution scenarios.
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Eric Chaumette, François Vincent, Olivier Besson. On ordered normally distributed vector parameter estimates. Signal Processing, Elsevier, 2015, vol. 115, pp. 20-26. ⟨10.1016/j.sigpro.2015.02.026⟩. ⟨hal-01414626⟩

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