Some inequalities for a LNQD sequence with applications

In this paper, some inequalities for a linearly negative quadrant dependent (LNQD) sequence are obtained. As their application, the asymptotic normality of the weight function estimate for a regression function is established, which extends the results of Roussas et al. (J. Multivar. Anal. 40:162-291, 1992) and Yang (Acta. Math. Sin. Engl. Ser. 23(6):1013-1024, 2007) for the strong mixing case to the LNQD case.