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@article{561855, author = {Řezáč, Martin}, article_location = {Bratislava}, article_number = {2}, keywords = {Kernel; density; estimate; bandwidth; maximal smoothing principle}, language = {eng}, issn = {1335-3632}, journal = {Journal of Electrical Engineering}, title = {Maximal Smoothing}, volume = {54}, year = {2003} }
TY - JOUR ID - 561855 AU - Řezáč, Martin PY - 2003 TI - Maximal Smoothing JF - Journal of Electrical Engineering VL - 54 IS - 2 SP - 44-46 EP - 44-46 PB - Slovak University of Technology SN - 13353632 KW - Kernel KW - density KW - estimate KW - bandwidth KW - maximal smoothing principle N2 - 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. ER -
ŘEZÁČ, Martin. Maximal Smoothing. \textit{Journal of Electrical Engineering}. Bratislava: Slovak University of Technology, 2003, vol.~54, No~2, p.~44-46. ISSN~1335-3632.
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