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June, 1990 On the Density of Minimum Contrast Estimators
Ib M. Skovgaard
Ann. Statist. 18(2): 779-789 (June, 1990). DOI: 10.1214/aos/1176347625


Conditions for the existence of the density of a minimum contrast estimator in a parametric statistical family are given together with a formula for this density. The formula is exact if multiple local minima cannot occur; otherwise the formula is an exact expression for the point process of local minima of the contrast function. Although it is not in general feasible to compute the expression for the density, the formula can be used as a basis for further expansion of the large deviation type. When the estimate is sufficient, either in the original model or after conditioning on an approximate or exact ancillary, the formula simplifies drastically. In particular, it is shown how Barndorff-Nielsen's formula for the density of the maximum likelihood estimator given an ancillary statistic is derived from the formula given here. In this way the nature of Barndorff-Nielsen's formula as an asymptotic approximation and its appearance as an exact formula for certain cases are demonstrated.


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Ib M. Skovgaard. "On the Density of Minimum Contrast Estimators." Ann. Statist. 18 (2) 779 - 789, June, 1990.


Published: June, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0709.62029
MathSciNet: MR1056336
Digital Object Identifier: 10.1214/aos/1176347625

Primary: 62F12
Secondary: 62E15

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 2 • June, 1990
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