方向数据核密度估计的大偏差和中偏差

Large deviations and moderate deviations for kernel estimator of density function of directional data

设X为取值于k-维单位球Ω的随机向量,密度函数为f(x),fn(x)=(nhk-1)-1[C(h)]·,x∈Ω为f(x)的核密度估计.通过计算Cramer泛函,分别得到了核密度估计在弱拓扑(L1,σ(L1,L∞))下的大偏差和中偏差.

Let X be a unit vector random variable taking values on a k - dimensional sphere Ω with probability density function f(x) . The problem considered is one of estimating f(x) base on n independent observation X1, X2,...,Xn on X ,Let fn(x) = (nhk-1}-1 is the estimator, consider a large de- viations and moderate deviations in for kernel estimator of density function of directional data