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The uniform empirical process under dependence in Holder norm

Dalila Merabet, Djamel Hamadouche

Abstract


Many statistical applications (change point, epidemic tests) in parametric and non parametric statistics are solved using the weak convergence of stochastic processes. The statistical procedures (estimation, testing statistics,...) are based on continuous functionals of paths of processes. Some processes useful in non parametric statistics (empirical process, quantile process,...) are studied in the Holder space which offers more continuous functionals than C[0, 1] for statistical applications. We consider the convolution smoothing of uniform empirical processes for dependent random variables (mixing, association) and we prove the weak Holder convergence to a generalized Brownian bridge.

Keywords


Association, Brownian bridge, empirical process, H¨older space, ρ-mixing, strong mixing, weak convergence

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