New Multivariate Product Density Estimators
نویسنده
چکیده
where X(k) = (X(k)1, . . . , X(k)d), and X(k) is the k-th nearest neighbor of x when points are ordered by increasing values of the product ∏d j=1 |xj−X(k)j |, and k = o(log n), k → ∞. The auxiliary results needed permit us to formulate universal consistency results (pointwise and in L1) for product kernel estimates with different window widths for each coordinate, and for rectangular partitioning and tree estimates. In particular, we show that locally adapted smoothing factors for product kernel estimates may make the kernel estimate inconsistent even under standard conditions on the bandwidths.
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