Kernel Density Estimation and Marginalisation (IN-) Consistency

Mike West
Institute of Statistic and Decision Sciences, Duke University

Nov 30 1988

Kernel density estimates, as commonly applied, generally have no exact, model based interpretation since they violate conditions that define coherent joint distributions. the issue of marginalization consistency is considered here. It is shown that most commonly used kernel functions violate this condition. It is also shown that marginalization consistency holds only for classes of kernel estimates based on Laplacian, or double-exponential kernels whose window width parameters are appropriately structured.


Kernel density estimation, Laplacian kernels, Marginalisation consistency, Predictive distributions


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