.svg){kind=logo}
UNIVARIATE AND BIVARIATE NONPARAMETRIC WIGNER SEMICIRCLE DENSITY ESTIMATORS: SIMULATION AND APPLICATION
Keywords:
Wigner semicircle distribution, kernel density estimator, smoothing parameter, differential scanning calorimetry.DOI:
https://doi.org/10.17654/0972361722053Abstract
In this paper, a new univariate and bivariate kernel density estimators using the Wigner semicircle distribution are introduced. The asymptotic bias; variance; mean squared error (MSE), integrated mean squared error (IMSE), and the optimal smoothing parameter are derived for both the univariate and bivariate cases. A simulation study is introduced to compare the performance of the proposed estimators with parametric distributions and other nonparametric estimators. Finally, a real data application of the measurements of differential scanning calorimetry is analyzed.
Received: May 5, 2022
Revised: June 15, 2022
Accepted: June 18, 2022
References
M. T. Chao and S. W. Cheng, Semicircle control chart for variables data, Quality Engineering 8(3) (1996), 441-446.
D. Chester, F. J. Taylor and M. Doyle, The Wigner distribution in speech processing applications, Journal of the Franklin Institute 318 (1984), 415-430.
D. Dragoman, Applications of the Wigner distribution function in signal processing, EURASIP Journal on Applied Signal Processing 10 (2005), 1520-1534.
V. A. Epanechnikov, Nonparametric estimation of multivariate probability density, Theory of Probability and its Application 14 (1969), 153-158.
M. E. Gorbunov, K. B. Lauritsen and S. S. Leroy, Application of Wigner distribution function for analysis of radio occultations, Radio Science 45 (2010), 1-11.
W. Härdle, M. Müller, S. Sperlich and A. Werwatz, Nonparametric and Semi-parametric Models: An Introduction, Springer-Verlag, New York, 2004.
A. H. Najmi, The Wigner distribution: A time-frequency analysis tool, Johns Hopkins APL Technical Digest 15 (1994), 298-305.
E. Parzen, On estimation of a probability density function and mode, The Annals of Mathematical Statistics 33 (1962), 1065-1076.
M. Rosenblatt, Remarks on some nonparametric estimates of density function, The Annals of Mathematical Statistics 27 (1956), 832-837.
J. S. Simonoff, Smoothing Methods in Statistics, Springer-Verlag, New York, 1996.
V. Todorov, S. Fidanova, I. Dimov and S. Poryazov, An optimized technique for Wigner kernel estimation, 16th Conference on Computer Science and Intelligence Systems, 2021, pp. 235-238.
Y. Van Nuland, ISO 9002 and the circle technique, Quality Engineering 5(2) (1992-93), 269-291.
M. P. Wand and M. C. Johnes, Kernel Smoothing, Chapman and Hall, London, 1995.
E. Wigner, On the quantum correction for thermodynamic equilibrium, Physical Review 40 (1932), 749-759.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
