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Biometrika 1978 65(3):489-496; doi:10.1093/biomet/65.3.489
© 1978 by Biometrika Trust
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Second-order sufficiency and statistical invariants

H. W. PEERS

Department of Statistics, University of Leeds

For samples from a regular distribution depending on one parameter a second-order sufficient statistic is introduced, and its characteristic function obtained correct to this order. With a canonical choice of parameter it is shown that the cumulants of this statistic are functions of basic statistical invariants including ‘curvature’ terms. The distribution of the maximum likelihood estimator given an approximate ancillary statistic is discussed for translation families and general distributions.

Key Words: Ancillary statistic • Conditional characteristic function • Maximum likelihood estimator • Second-order sufficiency • Statistical invariant


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