(Received March 13, 1995; revised October 9, 1995)
Abstract. f(x) is a univariate density in C4 with bounded support. For any n and sufficiently small kernel bandwidths, the symmetric appendage of any negative mass, -U, to any smooth unimodal symmetric kernel of order p = 2 shifts expected estimator mass from regions where f ''(x) > 0 to regions where f ''(x) < 0. For large n, the mean automatic kernel adaptation induced by -U is analyzed in the simplest MISE reduction scenario: The symmetric appendage of -U to the uniform kernel K(x, X) over MISE-optimal bandwidths reduces MISE by shifting K(x, X) mass asymmetrically across the observation X in the direction of decreasing |f ''(x)|.
Key words and phrases: Kernel adaptation, higher order kernels, induced kernel asymmetry.
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