Probability density function estimation by positive quartic C2-spline functions
Abstract
Spline is a continuous function piecewise-defined by polynomials and is widely used for interpolation and smoothing of observed data. In 1994, Heβ and Schmidt proposed a positive quartic C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -spline interpolation for estimation of a non-negative and twice continuously differentiable function. In this paper, first we generalize the positive quartic C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -spline interpolation to the positive quartic C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -spline smoothing. Then we propose two estimation methods of a probability density function from its histogram by extending the ideas of the positive quartic C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -spline interpolation and smoothing. Finally numerical experiments show the effectiveness of the proposed methods.
BibTeX
@inproceedings{icassp2015_probabilitydensi,
title = {Probability density function estimation by positive quartic C2-spline functions},
author = {Daichi Kitahara and Isao Yamada},
booktitle = {ICASSP 2015},
year = {2015}
}