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Consider the nonparametric regression model Y ni = g(x ni ) + ni for i = 1, . . . , n, where g is unknown, x ni are fixed design points, and 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).

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