This paper addresses the following question: How much information do the kernel function and the bandwidth provide for nonparametric kernel estimation? The question is addressed by showing that kernel estimation of a cumulative distribution function (CDF) is an information transmission procedure...

Kullback-Leibler information is widely used for developing indices of distributional fit. The most celebrated of such indices is Akaike’s AIC, which is derived as an estimate of the minimum Kullback-Leibler information between the unknown data-generating distribution and a parametric model. In...