In statistical analyses, especially those using a multiresponse regression model approach, mathematical that describes functional relationship between more than one response variables and or predictor is often involved. The these expressed by function. the nonparametric (MNR) part of model, estimating function becomes main problem, as there correlation responses such it necessary to include sym...

To develop spatially continuous seismicity models (earthquake probability distributions) from a given earthquake catalog, the method of kernel estimation has been suggested. Kernel estimations with a global (spatially invariant) bandwidth deal poorly with earthquake hypocenter distributions that have different spatially local features. For example, a typical earthquake catalog has several areas...

Masry (1996b) provides estimation bias and variance expression for a general local polynomial kernel estimator in a general multivariate regression framework. Under smoother conditions on the unknown regression and by including more refined approximation terms than that in Masry (1996b), we extend the result of Masry (1996b) to obtain explicit leading bias terms for the whole vector of the loca...

We investigate the performance of conventional bandwidth estimators for non-parametric kernel density estimation on a number of representative pattern-recognition tasks, to gain a better understanding of the behaviour of these estimators in high-dimensional spaces. We show that there are several regularities in the relative performance of conventional kernel bandwidth estimators across differen...

We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernelbased methodology in this setting, and discuss its basic properties. Then we point to close connections that exist between kernel methods and much newer approaches based on minimum contrast techniques. The connections are through use of the sinc kernel...

We continue the development of a method for the selection of a bandwidth or a number of design parameters in density estimation. We provide explicit non-asymptotic density-free inequalities that relate the L1 error of the selected estimate with that of the best possible estimate, and study in particular the connection between the richness of the class of density estimates and the performance bo...

• • ~~~~~~ In the setting of nonparametric multivariate density estimation, theorems are established which allow a comparison of the Kullback-Leibler and the Least Squares cross-validation methods of smoothing parameter selection. The family of delta sequence estimators (including kernel, orthogonal series, histogram and histospline estimators) is considered. These theorems also show that eithe...

We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient function...