Abstract:
In this paper, we obtain the strong uniform convergence rate
δn(
r) of estimatis of probability density
f(
x) and its derivatives
f(r)(
x), here \begingathered\delta_n(r)=\sup _-\infty<\infty<\infty\left|\hatf_n^(r)(x)-f^(r)(x)\right|, \hatf_n^(r)(x)=\frac1n \pi \sum_k=1^n\left\frac\sin \left\left(x-\infty_k\right) \varphi(n)\rightx-x_k\right_0^(r), \\ (r=0,1,2, \cdots),\endgathered,
xk(
k=1, 2,…,
n) are i.i.d. samples drawn from a population with density
f(
x), \varphi(n)>0, \lim _i \rightarrow \infty \varphi(n)=\infty,The asymptotic normalities are discussed.