The Annals of Statistics

Asymptotic efficiency of estimates for models with incidental nuisance parameters

Helmut Strasser

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In this paper we show that the well-known asymptotic efficiency bounds for full mixture models remain valid if individual sequences of nuisance parameters are considered. This is made precise both for some classes of random (i.i.d.) and nonrandom nuisance parameters. For the random case it is shown that superefficiency of the kind given by an example of Pfanzagl can happen only with low probability. The nonrandom case deals with permutation-invariant estimators under one-dimensional nuisance parameters. It is shown that the efficiency bounds remain valid for individual nonrandom arrays of nuisance parameters whose empirical process, if it is centered around its limit and standardized, satisfies a compactness condition. The compactness condition is satisfied in the random case with high probability. The results make use of basic LAN theory. Regularity conditions are stated in terms of $L^2$-differentiability.

Article information

Ann. Statist., Volume 24, Number 2 (1996), 879-901.

First available in Project Euclid: 24 September 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62A20 62B15: Theory of statistical experiments
Secondary: 62F05: Asymptotic properties of tests 62F12: Asymptotic properties of estimators

Regularity differentiability in quadratic mean sufficiency equivalence of experiments


Strasser, Helmut. Asymptotic efficiency of estimates for models with incidental nuisance parameters. Ann. Statist. 24 (1996), no. 2, 879--901. doi:10.1214/aos/1032894471.

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