On Boundary Correction in Kernel Estimation

The approximate expressions derived for the bias and variance of the log- transform kernel density estimation at point x, given in (14) and (17), sug- gest that the log-transform

For different classes of level sets (mainly star-shaped or convex level sets), estimators based on the excess mass approach were studied by Hartigan [8], M¨ uller [9], M¨ uller

A similar correction used in density estimation would be made for improve the theoretical performance of the usual kernel distribution function estimator at the boundary points..

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated-kernels in the nonparametric estima- tion for

It is shown that the estimates are consistent for all densities provided that the characteristic functions of the two kernels do not coincide in an open

Annales de l’Institut Henri Poincaré - Probabilités.. - Naturally to use all these estimates in our paper it suffices to write the Stratonovitch equations in Ito

More sepcifically, Ripley’s circumferential method (from Ripley (1976) and Ripley (1977)) is described in Section 2.5 and again, heuristics on the interpretation of the weights (in

Our goal is to investigate the asymptotic properties of a kernel density estimator asso- ciated with the driven noise of a linear regression in adaptive tracking and to propose