Concentration of empirical distribution functions with applications to non-i.i.d. models. (English) Zbl 1207.62106

Bobkov, S. G.; Götze, F.

Bernoulli 16, No. 4, 1385-1414 (2010).

Summary: The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincaré-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical distribution functions associated with high-dimensional random matrices.

MSC:

62G30	Order statistics; empirical distribution functions
62H10	Multivariate distribution of statistics
60E15	Inequalities; stochastic orderings
62E17	Approximations to statistical distributions (nonasymptotic)
60F10	Large deviations
15B52	Random matrices (algebraic aspects)

Keywords:

empirical measures; logarithmic Sobolev inequalities; Poincaré-type inequalities; random matrices; spectral distributions

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