概率密度函数及其导数的估计

CONVERGENCE RATE OF ESTIMATES OF PROBABILITY DENSITY FUNCTION AND ITS DERIVATIVES

本文研究一个对概率密度函数f(x)及其导数的估计,它基于Fourier变换方法上,被称为Fourier变换估计.我们讨论了这估计的相合性及渐近正态性,并用这方法对众数也进行了估计.

In this paper, we obtain the strong uniform convergence rate δ_n(r) of estimatis of probability density f(x) and its derivatives f^((r))(x), here x_k (k=1, 2,…, n) are i.i.d. samples drawn from a population with density f(x), The asymptotic normalities are discussed.