The $L_1$ Convergence of Kernel Density Estimates

Let $X_1, \cdots, X_n$ be a sequence of independent random vectors taking values in $\mathbf{\mathbb{R}}^d$ with a common probability density $f$ . If $f_n(x) = (1/h) h^{-d}_n\sum^n_{i = 1}K((x - X_i)/h_n)$ is the kernel estimate of $f$ from $X_1, \cdots, X_n$ then conditions on $K$ and $\{h_n\}$ are given which insure that $\int|f_n(x) - f(x)|dx \rightarrow_n 0$ in probability or with probability one. No continuity conditions are imposed on $f$ .Let $X_1, \cdots, X_n$ be a sequence of independent random vectors taking values in $\mathbf{\mathbb{R}}^d$ with a common probability density $f$. If $f_n(x) = (1/h) h^{-d}_n\sum^n_{i = 1}K((x - X_i)/h_n)$ is the kernel estimate of $f$ from $X_1, \cdots, X_n$ then conditions on $K$ and $\{h_n\}$ are given which insure that $\int|f_n(x) - f(x)|dx \rightarrow_n 0$ in probability or with probability one. No continuity conditions are imposed on $f$.

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笔记与分组

分类依据与纠错

The $L_1$ Convergence of Kernel Density EstimatesThe $L_1$ Convergence of Kernel Density Estimates

代码、数据与补充材料

核密度估计的L1收敛

原文摘要

同方向的基础文献

同方向的基础文献

分类依据与纠错

The L1L_1L1​ Convergence of Kernel Density EstimatesThe $L_1$ Convergence of Kernel Density Estimates

代码、数据与补充材料

核密度估计的L1收敛

原文摘要

同方向的基础文献

同方向的基础文献

The $L_1$ Convergence of Kernel Density EstimatesThe $L_1$ Convergence of Kernel Density Estimates