Rate of Strong Consistency of Two Nonparametric Density Estimators
两类非参数密度估计量的强一致收敛速度
Two nonparametric density estimators, based on Fourier series and the Fejer kernel, are presented. One of them $(\tilde{f}_N)$ is appropriate when the unknown density $f$ vanishes outside a known bounded interval; the other $(f_N^\sharp)$ is applicable without any assumptions about the support of $f$. The estimator $f_N^\sharp$ is of the type studied by Watson and Leadbetter (Sankhya A 26, 1964) and $\tilde{f}_N$ is almost of that type: both may be said to be of the "$\delta$…