The Uniform Convergence Rate of Kernel Density Estimate
Citation：
Yang Zhenhai.The Uniform Convergence Rate of Kernel Density Estimate[J].Chinese Annals of Mathematics B,1985,6(3):335~344
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Authors：
Yang Zhenhai;
Abstract：
In this paper, we study the uniform convergence rate of kernel density estimate [\hat f_n] and get optimal uniform rate of convergence without the assumption of compact support for kernel function. It is proved that if the density function f satisfies \lambda-condition and the kernel function K is \lambda-good (see section 1), then we have
limsup(\frac{n}{log n})^{\lambda/(1+2\lambda)}sup|[\hat f_n](x)-f(x)|\leq const. a.s.
