Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model

Estimation of probability density functions (pdf) is considered an essential part of statistical modelling. Heteroskedasticity and outliers are the problems that make data analysis harder. The Cauchy mixture model helps us to cover both of them. This paper studies five different significant types of...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Tomas Ruzgas, Mantas Lukauskas, Gedmantas Čepkauskas
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Cauchy mixture model nonparametric density estimation density estimation algorithms adapted kernel density estimate logspline estimation Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/29e6646bad8844408950269b9d70d474
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:29e6646bad8844408950269b9d70d474
record_format	dspace
spelling	oai:doaj.org-article:29e6646bad8844408950269b9d70d4742021-11-11T18:16:25ZNonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model10.3390/math92127172227-7390https://doaj.org/article/29e6646bad8844408950269b9d70d4742021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2717https://doaj.org/toc/2227-7390Estimation of probability density functions (pdf) is considered an essential part of statistical modelling. Heteroskedasticity and outliers are the problems that make data analysis harder. The Cauchy mixture model helps us to cover both of them. This paper studies five different significant types of non-parametric multivariate density estimation techniques algorithmically and empirically. At the same time, we do not make assumptions about the origin of data from any known parametric families of distribution. The method of the inversion formula is made when the cluster of noise is involved in the general mixture model. The effectiveness of the method is demonstrated through a simulation study. The relationship between the accuracy of evaluation and complicated multidimensional Cauchy mixture models (CMM) is analyzed using the Monte Carlo method. For larger dimensions (<i>d</i> ~ 5) and small samples (<i>n</i> ~ 50), the adaptive kernel method is recommended. If the sample is <i>n</i> ~ 100, it is recommended to use a modified inversion formula (MIDE). It is better for larger samples with overlapping distributions to use a semi-parametric kernel estimation and more isolated distribution-modified inversion methods. For the mean absolute percentage error, it is recommended to use a semi-parametric kernel estimation when the sample has overlapping distributions. In the smaller dimensions (<i>d</i> = 2) and a sample is with overlapping distributions, it is recommended to use the semi-parametric kernel method (SKDE) and for isolated distributions, it is recommended to use modified inversion formula (MIDE). The inversion formula algorithm shows that with noise cluster, the results of the inversion formula improved significantly.Tomas RuzgasMantas LukauskasGedmantas ČepkauskasMDPI AGarticleCauchy mixture modelnonparametric density estimationdensity estimation algorithmsadapted kernel density estimatelogspline estimationMathematicsQA1-939ENMathematics, Vol 9, Iss 2717, p 2717 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Cauchy mixture model nonparametric density estimation density estimation algorithms adapted kernel density estimate logspline estimation Mathematics QA1-939
spellingShingle	Cauchy mixture model nonparametric density estimation density estimation algorithms adapted kernel density estimate logspline estimation Mathematics QA1-939 Tomas Ruzgas Mantas Lukauskas Gedmantas Čepkauskas Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model
description	Estimation of probability density functions (pdf) is considered an essential part of statistical modelling. Heteroskedasticity and outliers are the problems that make data analysis harder. The Cauchy mixture model helps us to cover both of them. This paper studies five different significant types of non-parametric multivariate density estimation techniques algorithmically and empirically. At the same time, we do not make assumptions about the origin of data from any known parametric families of distribution. The method of the inversion formula is made when the cluster of noise is involved in the general mixture model. The effectiveness of the method is demonstrated through a simulation study. The relationship between the accuracy of evaluation and complicated multidimensional Cauchy mixture models (CMM) is analyzed using the Monte Carlo method. For larger dimensions (<i>d</i> ~ 5) and small samples (<i>n</i> ~ 50), the adaptive kernel method is recommended. If the sample is <i>n</i> ~ 100, it is recommended to use a modified inversion formula (MIDE). It is better for larger samples with overlapping distributions to use a semi-parametric kernel estimation and more isolated distribution-modified inversion methods. For the mean absolute percentage error, it is recommended to use a semi-parametric kernel estimation when the sample has overlapping distributions. In the smaller dimensions (<i>d</i> = 2) and a sample is with overlapping distributions, it is recommended to use the semi-parametric kernel method (SKDE) and for isolated distributions, it is recommended to use modified inversion formula (MIDE). The inversion formula algorithm shows that with noise cluster, the results of the inversion formula improved significantly.
format	article
author	Tomas Ruzgas Mantas Lukauskas Gedmantas Čepkauskas
author_facet	Tomas Ruzgas Mantas Lukauskas Gedmantas Čepkauskas
author_sort	Tomas Ruzgas
title	Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model
title_short	Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model
title_full	Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model
title_fullStr	Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model
title_full_unstemmed	Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model
title_sort	nonparametric multivariate density estimation: case study of cauchy mixture model
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/29e6646bad8844408950269b9d70d474
work_keys_str_mv	AT tomasruzgas nonparametricmultivariatedensityestimationcasestudyofcauchymixturemodel AT mantaslukauskas nonparametricmultivariatedensityestimationcasestudyofcauchymixturemodel AT gedmantascepkauskas nonparametricmultivariatedensityestimationcasestudyofcauchymixturemodel
_version_	1718431872013303808

Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model

Ejemplares similares