In this paper, we propose a new non-parametric density estimator derived from the theory of frames and Riesz bases. In particular, we propose the so-called bi-orthogonal density estimator based on the class of B-splines, and derive its theoretical properties including the asymptotically optimal...

We study a general and efficient nonparametric density estimation procedure for local bases, including B-splines, using a novel statistical Galerkin method, combined with basis duality theory. We provide an efficient cross-validation procedure to select the bandwidth, based on closed-form...

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 experienced recent advances in both theory and methodology. These estimators occupy a very interesting space in statistics,...

In this paper, we derive the closed form formulae for moments of Student's t-distribution in the one dimensional case as well as in higher dimensions through a unified probability framework. Interestingly, the closed form expressions for the moments of Student's t-distribution can be written in...