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Article Dans Une Revue Mathematical Methods of Statistics Année : 2019

Central Limit Theorems for Conditional Empirical and Conditional U-Processes of Stationary Mixing Sequences

Résumé

In this paper we are concerned with the weak convergence to Gaussian processes of conditional empirical processes and conditional U-processes from stationary β-mixing sequences indexed by classes of functions satisfying some entropy conditions. We obtain uniform central limit theorems for conditional empirical processes and conditional U-processes when the classes of functions are uniformly bounded or unbounded with envelope functions satisfying some moment conditions. We apply our results to introduce statistical tests for conditional independence that are multivariate conditional versions of the Kendall statistics.
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Dates et versions

hal-02300780 , version 1 (29-09-2019)

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Salim Bouzebda, B. Nemouchi. Central Limit Theorems for Conditional Empirical and Conditional U-Processes of Stationary Mixing Sequences. Mathematical Methods of Statistics, 2019, 28 (3), pp.169-207. ⟨10.3103/S1066530719030013⟩. ⟨hal-02300780⟩
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