Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 2, 292-297

ASYMPTOTIC PROPERTIES OF UNBIASED ESTIMATORS IN THE NATURAL EXPONENTIAL FAMILY WITH QUADRATIC VARIANCE FUNCTION

By

F. LÓPEZ-BLÁZQUEZ, Universidad de Sevilla, Spain

and

A. CASTAÑO-MARTÍNEZ, Universidad de Cádiz, Spain

SUMMARY. By using orthogonal expansions, we derive the asymptotic properties of the minimum variance unbiased estimator, (MVU), of a function of the mean, h m , in the natural exponential family with quadratic variance function. The limit behavior depends on j=j( m 0), the order of the first non-zero derivative at the true value of the parameter, m 0.

AMS (1991) subject classification. Primary 62F12; secondary 62F10.

Key words and phrases. Orthogonal expansions; Hermite polynomials.

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