Kernel-Type estimation of bivariate distribution for associated random variables

• Autor(es): Azevedo, Cecília Maria ; Oliveira, Paulo
• Data: 2000
• Identificador Persistente: http://hdl.handle.net/1822/2014
• Origem: RepositóriUM - Universidade do Minho
• Assunto(s): Association; Convergence; Kernel estimation; Stationarity
• Tipo de Documento: Documento de conferência
• Idioma: Inglês

Descrição

Let a stationary sequence of associated random variables with uniform distribution on [0,1] and F the distribution function of the random pair (X_1,X_{k+1}), for fixed k. We introduce a kernel estimator for F and study its asymptotic properties and moments, characterizing their convergence rates. From these we derive the optimal rate for the bandwidth, which is of order n up -1. Conditions are also given to ensure that the finite dimensional distributions are asymptotically gaussian.