Kernel-Type estimation of bivariate distribution for associated random variables

• Author(s): Azevedo, Cecília Maria ; Oliveira, Paulo
• Date: 2000
• Persistent ID: http://hdl.handle.net/1822/2014
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Association; Convergence; Kernel estimation; Stationarity
• Document Type: Conference Object
• Language: English

Description

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.