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Title: Strong convergence rates for the estimation of a covariance operator for associated samples
Authors: Henriques, Carla 
Oliveira, Paulo 
Issue Date: 2008
Citation: Statistical Inference for Stochastic Processes. 11:1 (2008) 77-91
Abstract: Abstract Let X n , n = 1, be a strictly stationary associated sequence of random variables, with common continuous distribution function F. Using histogram type estimators we consider the estimation of the two-dimensional distribution function of (X 1,X k+1) as well as the estimation of the covariance function of the limit empirical process induced by the sequence X n , n = 1. Assuming a convenient decrease rate of the covariances Cov(X 1,X n+1), n = 1, we derive uniform strong convergence rates for these estimators. The condition on the covariance structure of the variables is satisfied either if Cov(X 1,X n+1) decreases polynomially or if it decreases geometrically, but as we could expect, under the latter condition we are able to establish faster convergence rates. For the two-dimensional distribution function the rate of convergence derived under a geometrical decrease of the covariances is close to the optimal rate for independent samples.
DOI: 10.1007/s11203-006-9007-3
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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