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A note on incomplete and boundedly complete families of discrete distributions

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  • Purkayastha Sumitra

Abstract

We present a general result giving us families of incomplete and boundedly complete families of discrete distributions. For such families, the classes of unbiased estimators of zero with finite variance and of parametric functions which will have uniformly minimum variance unbiased estimators with finite variance are explicitly characterized. The general result allows us to construct a large number of families of incomplete and boundedly complete families of discrete distributions. Several new examples of such families are described.

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  • Purkayastha Sumitra, 2009. "A note on incomplete and boundedly complete families of discrete distributions," Statistics & Risk Modeling, De Gruyter, vol. 27(4), pages 227-234, December.
    • Handle: RePEc:bpj:strimo:v:27:y:2009:i:4:p:227-234:n:3
    DOI: 10.1524/stnd.2009.1046
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    References listed on IDEAS

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    1. S. Bar-Lev & D. Plachky, 1989. "Boundedly complete families which are not complete," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 331-336, December.
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