This work reviews the literature on spline local basis methods for non-parametric density
estimation. Particular attention is paid to B-spline density estimators which have …

Density estimation for observational data plays an integral role in a broad spectrum of
applications, eg, statistical data analysis and information-theoretic image registration. Of …

In this article, we propose a new nonparametric density estimator derived from the theory of
frames and Riesz bases. In particular, we propose the so-called bi-orthogonal density …

A general and efficient nonparametric density estimation procedure for local bases,
including B-splines, is proposed, which employs a novel statistical Galerkin method …

Complex data such as those where each statistical unit under study is described not by a
single observation (or vector variable), but by a unit-specific sample of several or even many …

Shape representation and retrieval of stored shape models are becoming increasingly more
prominent in fields such as medical imaging, molecular biology and remote sensing. We …

We propose a non‐linear density estimator, which is locally adaptive, like wavelet
estimators, and positive everywhere, without a log‐or root‐transform. This estimator is based …

This thesis considers the application of wavelet methods to a selection of problems arising in
non-stationary time series analysis and Poisson regression. In the rst part of the thesis, we …

We introduce a new approach to shape-preserving estimation of cumulative distribution
functions and probability density functions using the wavelet methodology for multivariate …

This paper addresses the problem of choosing the optimal number of basis functions in
constructing wavelet series density estimators. It is well known that projection estimators …