Asymptotic Behaviors of Some Measures of Accuracy in Nonparametric Curve Estimation with Dependent Observations

Under the i.i.d. condition, Marron and Härdle (1986, J. Multivariate Anal.20 91-113) showed that quadratic measures of errors for nonparametric kernel estimates are asymptotically equivalent, and Hall (1984, J. Multivariate Anal.14 1-16) investigated their convergence rates. In this article, we extend their results to the dependent case. In addition, the effect of dimension on the convergence rates will be discussed.