Bias Correction and Higher Order Kernel Functions

Jianqing Fan Department of Statistics University of North Carolina Chapel Hill, N.C. 27514 Kernel density estimates are frequently used, based on a second order kernel. Thus, the bias inherent to the estimates has an order of O(h~). In this note, a method of corr~cting the bias in the kernel density estimates is provided, which reduces the bias to a smaller order. Effectively, this method produces a higher order kernel based on a second order kernel. For a kernel function K, the functions and 1 K(lc-l)( )/ f~oo K(lc-l)(z)/zdz z z are kernels of order k, under some mild conditions. lCompleted while visiting Department of Statistics, University of North Carolina, Chapel Hill. Abbreviated title. Bias Correction. AMS 1980 subject classification. Primary 62G05. Secondary 62G20.