Abstract:

Let {ε_i,1≤i≤n} be negatively dependent and random error sequence. With the help of the nonparametric regression model Y_i=g(x_i)+ε_i(1≤i≤n), we discussed the rate of the strong consistency of the nonparametric regression weighted function estimator g_n(x) for negatively dependent samples using Bernstein inequality. The consistency was extended to the case of negatively dependent samples.

Key words: negatively dependent sequence, nonparametric regression, weighted kernel estimator, rate of strong consistency