THE UNIFORM CONVERGENCE RATE OF KERNEL DENSITY ESTIMATE

In this paper,we study the uniform convergence rate of kernel density estimate f_nand get optimal uniform rate of convergence without the assumption of compact supportfor kernel function.It is proved that if the density function f satisfies λ-condition andthe kernel function K is λ-good(see section 1),then we havelimsup (n/(logn))~(λ/(1+2λ))丨_n(x)-f(x)丨≤const,a.s.

The Uniform Convergence Rate of Kernel Density Estimate

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.