Estimating a Distribution Function

Rudolf Beran

doi:10.1214/aos/1176343806

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Home > Journals > Ann. Statist. > Volume 5 > Issue 2 > Article

March, 1977 Estimating a Distribution Function

Rudolf Beran

Ann. Statist. 5(2): 400-404 (March, 1977). DOI: 10.1214/aos/1176343806

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Abstract

It is shown that the limiting distribution of any regular estimator of a continuous cdf on [0, 1] can be represented as a convolution of the Brownian bridge process with another distribution on $C\lbrack 0, 1\rbrack$. The result is related to Hajek's representation for limiting distributions of regular parametric estimators.