On location and scale maximum likelihood estimators

Gupta, A. K.; Székely, G. J.

doi:10.1090/S0002-9939-1994-1207537-3

On location and scale maximum likelihood estimators
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by A. K. Gupta and G. J. Székely PDF

Proc. Amer. Math. Soc. 120 (1994), 585-589 Request permission

Abstract:

The maximum likelihood estimators of location and scale parameters have the following undesirable properties: (i) they are not always consistent, and (ii) the asymptotic correlation of the MLE’s of the "unrelated" location and scale parameters can be arbitrarily close to one. In this paper methods to overcome these undesirable properties have been studied.

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Probability theory