CENTRAL LIMIT THEORMS IN C[0,1] FOR A CLASS OF ESTIMATORS OF A DISTRIBUTION FUNCTION

R. Nixdorf

Statistica Neerlandica, 1985, vol. 39, issue 3, 251-260

Abstract: As non–parametric estimates of an unknown distribution function (d.f.) F based on i.i.d. observations X1 Xn with this d.f. are used, where Hn is a sequence of d.f.'s converging weakly to the unit mass at zero. Under regularity conditions on F and the sequence (Hn) it is shown that √n(Fn–F) and √n(Rn– F) in C[0,1] converge in distribution to a process G with G(t) =W° (F(t)), where W° is a Brownian bridge in C[0,1]. Further the a.s. uniform convergence of R., is considered and some examples are given.

Date: 1985
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