Abstract
Precise asymptotic behavior for mean integrated squared error (MISE) is determined for sequences of kernel estimators of a density in a broad class, including discontinuous and possibly unbounded densities. The paper shows that the sequence using the kernel optimal at each fixed sample size is asymptotically more efficient than a sequence generated by changing the bandwidth of a fixed kernel shape, regardless of the kernel shape. The class of densities considered are those whose characteristic functions behave at large arguments like the product of a Fourier series and a regularly varying function. This condition may be related to the smoothness of an m-th derivative of the density.
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Partially supported by National Science Foundation Grant DMS-8711924.
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Cline, D.B.H. Optimal kernel estimation of densities. Ann Inst Stat Math 42, 287–303 (1990). https://doi.org/10.1007/BF00050838
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DOI: https://doi.org/10.1007/BF00050838