Let fnh be the Parzen-Rosenblatt kernel estimate of a density f on the real line, based upon a sample of n i.i.d. random variables drawn from f , and with smoothing factor h. Let gnh be another kernel estimate based upon the same data, but with a different kernel. We choose the smoothing factor H so as to minimize ∫ |fnh− gnh|, and study the properties of fnH and gnH . It is shown that the esti...

In brain imaging analysis, there is a need for analyzing data collected on the cortical surface of the human brain. Gaussian kernel smoothing has been widely used in this area in conjunction with random field theory for analyzing data residing in Euclidean spaces. The Gaussian kernel is isotropic in Euclidian space so it assigns the same weights to observations equal distance apart. However, wh...

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. For example, in estimating the difference between two densities, we show that the optimal smoothing parameters are increasing functions of the sample size of the complementary group. A relative newc...

The asymptotic properties of smoothing parameter estimates for smoothing splines are developed. We consider a variety of estimates including Generalized Cross Validation, Generalized Maximum Likelihood, and more generally Type II ML estimates and the properties of the marginal posterior mode. Under the usual Sobolov space frequentist assumptions on the function to be estimated , consistency and...

Convolutional Radial Basis Function (RBF) networks are introduced for smoothing out irregularly sampled signals. Our proposed technique involves training a RBF network and then convolving it with a Gaussian smoothing kernel in an analytical manner. Since the convolution results in an analytic form, the computation necessary for numerical convolution is avoided. Convolutional RBF networks need t...

Kernel based learning has found wide applications in several data mining problems. In this paper, we propose a modified classical linear kernel using an automatic smoothing parameter (Sp) selection compared with the existing approach. We designed the Sp values using the Eigen values computed from the dataset. Experiment results using some classification related benchmark datasets reveal that th...