On Recursive Estimates of Probability Density and Regression Line

Recursive estimates for the probability density and regression line are set up on the basis of nonparametric probability-density estimates of the Rosenblatt–Parzen type [Ann. Math. Stat., 33, No. 3, 1065–1076 (1965); 27, No. 3, 832–835 (1956)]; their asymptotic properties (as $n\to\infty$) are investigated, and, in particular, it is shown that they are asymptotically normal; results of statistical simulation of ordinary and recursive estimates of the regression line are given.