Optimal Choice of the Kernel Function for the Parzen Kernel-type Density Estimators
| dc.citation.bibtexName | techreport | en_US |
| dc.citation.issueNumber | TR7501 | en_US |
| dc.citation.journalTitle | Rice University ECE Technical Report | en_US |
| dc.contributor.author | Kazakos, D. | en_US |
| dc.date.accessioned | 2007-10-31T00:49:11Z | en_US |
| dc.date.available | 2007-10-31T00:49:11Z | en_US |
| dc.date.issued | 1975-04-20 | en_US |
| dc.date.modified | 2003-10-22 | en_US |
| dc.date.submitted | 2003-08-18 | en_US |
| dc.description | Tech Report | en_US |
| dc.description.abstract | Let W<sub>p</sub><sup>(2)</sup> be the Sobolev space of probability density functions f(X) whose first derivative is absolutely continuous and whose second derivative is in L<sub>p</sub>(- ∞ ,+ ∞), for p ∈ [1, + ∞]. Using an upper bound to the mean square error for a fixed X E [f(X) - f<sub>n</sub>(X)0]<sup>2</sup>, found by G. Wahba, where f<sub>n</sub>(X) is the Parzen Kernel-type estimate of f(X), we find the finite support Kernel function K(X) that minimizes the said upper bound. The optimal Kernel funciton is: K(y) = (1+a<sup>-1</sup>) (2T)<sup>-1</sup> [1-T<sup>-a</sup> |y|<sup>a</sup>], for |y|<T where [-T,T] is the support interval, and a=2-p<sup>-1</sup>. | en_US |
| dc.identifier.citation | D. Kazakos, "Optimal Choice of the Kernel Function for the Parzen Kernel-type Density Estimators," <i>Rice University ECE Technical Report,</i> no. TR7501, 1975. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/20004 | en_US |
| dc.language.iso | eng | en_US |
| dc.subject | kernel | en_US |
| dc.subject | parzen | en_US |
| dc.subject.keyword | kernel | en_US |
| dc.subject.keyword | parzen | en_US |
| dc.title | Optimal Choice of the Kernel Function for the Parzen Kernel-type Density Estimators | en_US |
| dc.type | Report | en_US |
| dc.type.dcmi | Text | en_US |
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