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

Consider the nonparametric regression model Yni=g(xni)+εni for i=1,…,n, where g is unknown, xni are fixed design points, and εni are negatively associated random errors. Nonparametric estimator gn(x) of g(x) will be introduced and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of gn(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).