【摘要】 设X为取值于k维单位球面上的单位随机向量,具有概率密度函数f（x）,X₁,…,X_n为X的n个i.i.d.的观察,讨论f（x）具有形式的核估计,其中K为定义于[0,+∞]上的非负核函数,ω_k为Ω_k上的Lebesque测度,本文建立了fn（x）的对数律,并给出了fn（x）的一致强相合速度。更多还原

【Abstract】 Let X be a random vector taking values on a k-dimensional unit sphere with probability density function (p.d.f.) /(x), and X1,...,Xn be a list of independent and identically distributed (i.i.d.) observations from X. The kernel estimator of f(x)considered here is of the form fn(x) = . where K is a kernelfunction defined on [0,+∞), ωk is the Lebesgue measure on Ωk. In this paper, we establish the uniformly strong consistency rates of fn(x) by deriving a law of the Logarithm for it.更多还原