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A \skewing" method is shown to e ectively reduce the order of bias of locally parametric estimators, and at the same time retain positivity properties. The technique involves rst calculating the usual locally parametric approximation in the neighbourhoodof a point x 0 that is a short distance from the place x where the we wish to estimate the density, and then evaluating this approximation at x. By way of comparison, the usual locally parametric approach takes x 0 = x. In our construction, x 0doi:10.2307/3318637 fatcat:qikryguw3rbfpdfuk5x5mllnba