Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences

Abstract

Consider the nonparametric regression model Y ni = g ( x ni ) + ε ni for i = 1 , … , n , where g is unknown, x ni are fixed design points, and ε ni are negatively associated random errors. Nonparametric estimator g n ( x ) of g ( x ) will be introduced and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of g n ( x ) and its asymptotic normality will be investigated. This extends the earlier work on independent random errors (e.g. see J. Multivariate Anal. 25(1) (1988) 100).