Empirical Processes and p-variation

R. M. Dudley
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R. M. Dudley: Massachusetts Institute of Technology, Mathematics Department

Chapter 13 in Festschrift for Lucien Le Cam, 1997, pp 219-233 from Springer

Abstract: Abstract Remainder bounds in Fréchet differentiability of functionals for p-variation norms are found for empirical distribution functions. For $$ 1 \leqslant p \leqslant 2$$ the p-variation of the empirical process n1/2(Fn — F) is of order n1-p/2 in probability up to a factor (log log n) p /2. For $$ \left( {F,G} \right) \mapsto \int {FdG}$$ and for $$ \left( {F,G} \right) \mapsto F \circ {{G}^{{ - 1}}}$$ this yields nearly optimal remainder bounds. Also, p-variation gives new proofs for the asymptotic distributions of the Cramér-von Mises-Rosenblatt and Watson two-sample statistics when the two sample sizes m, n go to infinity arbitarily.

Keywords: Outer Probability; Asymptotic Distribution; Empirical Process; Empirical Distribution Function; Brownian Bridge (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1880-7_13

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DOI: 10.1007/978-1-4612-1880-7_13

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