Exponential inequality for a class of NOD random variables and its application

In this paper, an exponential inequality for weighted sums of identically distributed NOD (negatively orthant dependent) random variables is established, by which we obtain the almost sure convergence rate O (1) n −1/2 (log n ) 1/2 of , which reaches the available one for independent random variables in terms of Berstein type inequality. As application, we obtain the relevant exponential inequality for Priestley-Chao estimator of nonparametric regression estimate under NOD samples, from which the strong consistency rate O (1) n −1/2 h n −1 (log n ) 1/2 s also obtained.