| Title |
Comparative evaluation of nonparametric density estimators for Gaussian mixture models with clustering support |
| Authors |
Ruzgas, Tomas ; Stankevičius, Gintaras ; Narijauskaitė, Birutė ; Arnastauskaitė Zencevičienė, Jurgita |
| DOI |
10.3390/axioms14080551 |
| Full Text |
|
| Is Part of |
Axioms.. Basel : MDPI. 2025, vol. 14, iss. 8, art. no. 551, p. 1-20.. ISSN 2075-1680 |
| Keywords [eng] |
univariate probability density ; nonparametric estimation ; Monte Carlo method |
| Abstract [eng] |
The article investigates the accuracy of nonparametric univariate density estimation methods applied to various Gaussian mixture models. A comprehensive comparative analysis is performed for four popular estimation approaches: adaptive kernel density estimation, projection pursuit, log-spline estimation, and wavelet-based estimation. The study is extended with modified versions of these methods, where the sample is first clustered using the EM algorithm based on Gaussian mixture components prior to density estimation. Estimation accuracy is quantitatively evaluated using MAE and MAPE criteria, with simulation experiments conducted over 100,000 replications for various sample sizes. The results show that estimation accuracy strongly depends on the density structure, sample size, and degree of component overlap. Clustering before density estimation significantly improves accuracy for multimodal and asymmetric densities. Although no formal statistical tests are conducted, the performance improvement is validated through non-overlapping confidence intervals obtained from 100,000 simulation replications. In addition, several decision-making systems are compared for automatically selecting the most appropriate estimation method based on the sample’s statistical features. Among the tested systems, kernel discriminant analysis yielded the lowest error rates, while neural networks and hybrid methods showed competitive but more variable performance depending on the evaluation criterion. The findings highlight the importance of using structurally adaptive estimators and automation of method selection in nonparametric statistics. The article concludes with recommendations for method selection based on sample characteristics and outlines future research directions, including extensions to multivariate settings and real-time decision-making systems. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
