Maximal Smoothing

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Authors	ŘEZÁČ Martin
Year of publication	2003
Type	Article in Periodical
Magazine / Source	Journal of Electrical Engineering
MU Faculty or unit	Faculty of Science
Citation
Field	Applied statistics, operation research
Keywords	Kernel; density; estimate; bandwidth; maximal smoothing principle
Description	Nonparametric density estimates attempt to reconstruct the probability density from which a random sample has come. A large part of the literature on density estimation is concerned with the issue of how to choose the degree of smoothness of the estimate. This paper describes the principle of maximal smoothing. The formula for asymptotically optimal bandwidth $h_f$ with respect to MISE is well-known. This formula depends on $\integral(f^{(k)}(x))^2dx$ reciprocally, where $f$ is an unknown probability density function. Our goal will be to make this integral as small as possible. Then we obtain the upper boundary for the bandwidth. The prsented paper is dealing with this procedure.
Related projects:	Functional-differential equations and mathematical-statistical models