Kazakos, D.2007-10-312007-10-311975-04-202003-08-18D. Kazakos, "Optimal Choice of the Kernel Function for the Parzen Kernel-type Density Estimators," <i>Rice University ECE Technical Report,</i> no. TR7501, 1975.https://hdl.handle.net/1911/20004Tech ReportLet 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>.engkernelparzenOptimal Choice of the Kernel Function for the Parzen Kernel-type Density EstimatorsReportkernelparzen