arXiv subjects

Vitaliy Oryshchenko

Publications and source records attributed to Vitaliy Oryshchenko.

3 recordsLinked to original sources

arXiv2018

Exact mean integrated squared error and bandwidth selection for kernel distribution function estimators

An exact, closed form, and easy to compute expression for the mean integrated squared error (MISE) of a kernel estimator of a normal mixture cumulative distribution function is derived for the class of arbitrary order Gaussian-based kernels. Comparisons are made with MISE of the empirical distribution function, the infeasible minimum MISE of kernel estimators, and the asymptotically optimal second order uniform kernel. The results afford straightforward extensions to other classes of kernel functions and distributions. The analysis also offers a guide on when to use higher order kernels in distribution function estimation. A simple plug-in method of simultaneously selecting the optimal bandwidth and kernel order is proposed based on a non-asymptotic approximation of the unknown distribution by a normal mixture. A simulation study shows that the method works well in finite samples, thus providing a viable alternative to existing bandwidth selection procedures.

stat.ME↗

arXiv2018

Improved Density and Distribution Function Estimation

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due to the systematic use of this extra information. The particular interest here is the estimation of densities or distributions of (generalised) residuals in semi-parametric models defined by a finite number of moment restrictions. Such estimates are of great practical interest, being potentially of use for diagnostic purposes, including tests of parametric assumptions on an error distribution, goodness-of-fit tests or tests of overidentifying moment restrictions. The paper gives conditions for the consistency and describes the asymptotic mean squared error properties of the kernel density and distribution estimators proposed in the paper. A simulation study evaluates the small sample performance of these estimators. Supplements provide analytic examples to illustrate situations where kernel weighting provides a reduction in variance together with proofs of the results in the paper.

stat.ME↗

arXiv2016

Indirect Maximum Entropy Bandwidth

This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in classical parametric models. The proposed estimators are designed to indirectly maximise the entropy of the leave-one-out kernel estimates of a distribution function, which are the analogues of the parametric probability integral transforms. The estimators based on minimisation of the Cramer-von Mises discrepancy, near-solution of the moment-based estimating equations, and inversion of the Neyman smooth test statistic are discussed and their performance compared in a simulation study. The bandwidth minimising the Anderson-Darling statistic is found to perform reliably for a variety of distribution shapes and can be recommended in practice. The results will also be of interest to anyone analysing the cross-validation bandwidths based on leave-one-out estimates or evaluation of nonparametric density forecasts.

stat.ME↗