On estimation of a functional of a probability density function. (English) Zbl 0784.62031
Summary: The problem of estimating the integral of the square of a probability density function is considered. It is shown that under some regularity conditions the kernel estimate of this functional is asymptotically normally distributed. An expression for the smoothing parameter that minimizes the mean square error of the estimate is derived. Results of simulation studies are included.
MSC:
62G07 | Density estimation |
62G20 | Asymptotic properties of nonparametric inference |
62E20 | Asymptotic distribution theory in statistics |
60F05 | Central limit and other weak theorems |