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

摘要

Consider the nonparametric regression model Y-ni=g(x(ni))+epsilon(ni) for i=1, n, where g is unknown, x(ni) are fixed design points, and epsilon(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). (C) 2004 Published by Elsevier Inc.