Density estimates of low bias

Two methods are given for adapting a kernel density estimate to obtain an estimate of a density function with bias O(h <Superscript> p </Superscript>) for any given p, where h=h(n) is the bandwidth and n is the sample size. The first method is standard. The second method is new and involves use of Bell polynomials. The second method is shown to yield smaller biases and smaller mean squared errors than classical kernel density estimates and those due to Jones et al. (Biometrika 82:327–338, <CitationRef CitationID="CR15">1995</CitationRef>). Copyright Springer-Verlag 2013