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Title: Convergence rates for the estimation of two-dimensional distribution functions under association and estimation of the covariance of the limit empirical process
Authors: Henriques, Carla 
Oliveira, Paulo Eduardo 
Issue Date: 2006
Citation: Journal of Nonparametric Statistics - Taylor & Francis. 18:2 (2006) 119-128
Abstract: Let Xn, n=1, be an associated and strictly stationary sequence of random variables, having marginal distribution function F. The limit in distribution of the empirical process, when it exists, is a centred Gaussian process with covariance function depending on terms of the form ?k(s, t)=P(X1 s, Xk+1 t)-F(s)F(t). We prove the almost sure consistency for the histogram to estimate each ?k and also to estimate the covariance function of the limit empirical process, identifying, for both, uniform almost sure convergence rates. The convergence rates depend on a suitable version of an exponential inequality. The rates obtained, assuming the covariances to decrease geometrically, are of order n-1/3log2/3nfor the estimator of ?k and of order n-1/3log5/3nfor the estimator of the covariance function.
DOI: 10.1080/10485250500466119
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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