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Robust mixture regression modeling based on the normal mean-variance mixture distributions. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107661] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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2
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Sugasawa S, Kobayashi G. Robust fitting of mixture models using weighted complete estimating equations. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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3
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Seemingly unrelated clusterwise linear regression for contaminated data. Stat Pap (Berl) 2022. [DOI: 10.1007/s00362-022-01344-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
AbstractClusterwise regression is an approach to regression analysis based on finite mixtures which is generally employed when sample observations come from a population composed of several unknown sub-populations. Whenever the response is continuous, Gaussian clusterwise linear regression models are usually employed. Such models have been recently robustified with respect to the possible presence of mild outliers in the sub-populations. However, in some fields of research, especially in the modelling of multivariate economic data or data from the social sciences, there may be prior information on the specific covariates to be considered in the linear term employed in the prediction of a certain response. As a consequence, covariates may not be the same for all responses. Thus, a novel class of multivariate Gaussian linear clusterwise regression models is proposed. This class provides an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that let the researcher free to use a different vector of covariates for each response. Details about the model identification and maximum likelihood estimation via an expectation-conditional maximisation algorithm are given. The performance of the new models is studied by simulation in comparison with other clusterwise linear regression models. A comparative evaluation of their effectiveness and usefulness is provided through the analysis of a real dataset.
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Sepahdar A, Madadi M, Balakrishnan N, Jamalizadeh A. Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions. Stat (Int Stat Inst) 2022. [DOI: 10.1002/sta4.421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Afsaneh Sepahdar
- Department of Statistics, Faculty of Mathematics and Computer Shahid Bahonar University of Kerman Kerman 76169‐14111 Iran
| | - Mohsen Madadi
- Department of Statistics, Faculty of Mathematics and Computer Shahid Bahonar University of Kerman Kerman 76169‐14111 Iran
| | | | - Ahad Jamalizadeh
- Department of Statistics, Faculty of Mathematics and Computer Shahid Bahonar University of Kerman Kerman 76169‐14111 Iran
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5
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Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2021.107182] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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6
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de Carvalho FDA, Lima Neto EDA, da Silva KC. A clusterwise nonlinear regression algorithm for interval-valued data. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2020.10.054] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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7
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Covariance matrix estimation of the maximum likelihood estimator in multivariate clusterwise linear regression. STAT METHOD APPL-GER 2021. [DOI: 10.1007/s10260-020-00523-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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8
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Bagnato L, Punzo A. Unconstrained representation of orthogonal matrices with application to common principal components. Comput Stat 2020. [DOI: 10.1007/s00180-020-01041-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
AbstractMany statistical problems involve the estimation of a $$\left( d\times d\right) $$
d
×
d
orthogonal matrix $$\varvec{Q}$$
Q
. Such an estimation is often challenging due to the orthonormality constraints on $$\varvec{Q}$$
Q
. To cope with this problem, we use the well-known PLU decomposition, which factorizes any invertible $$\left( d\times d\right) $$
d
×
d
matrix as the product of a $$\left( d\times d\right) $$
d
×
d
permutation matrix $$\varvec{P}$$
P
, a $$\left( d\times d\right) $$
d
×
d
unit lower triangular matrix $$\varvec{L}$$
L
, and a $$\left( d\times d\right) $$
d
×
d
upper triangular matrix $$\varvec{U}$$
U
. Thanks to the QR decomposition, we find the formulation of $$\varvec{U}$$
U
when the PLU decomposition is applied to $$\varvec{Q}$$
Q
. We call the result as PLR decomposition; it produces a one-to-one correspondence between $$\varvec{Q}$$
Q
and the $$d\left( d-1\right) /2$$
d
d
-
1
/
2
entries below the diagonal of $$\varvec{L}$$
L
, which are advantageously unconstrained real values. Thus, once the decomposition is applied, regardless of the objective function under consideration, we can use any classical unconstrained optimization method to find the minimum (or maximum) of the objective function with respect to $$\varvec{L}$$
L
. For illustrative purposes, we apply the PLR decomposition in common principle components analysis (CPCA) for the maximum likelihood estimation of the common orthogonal matrix when a multivariate leptokurtic-normal distribution is assumed in each group. Compared to the commonly used normal distribution, the leptokurtic-normal has an additional parameter governing the excess kurtosis; this makes the estimation of $$\varvec{Q}$$
Q
in CPCA more robust against mild outliers. The usefulness of the PLR decomposition in leptokurtic-normal CPCA is illustrated by two biometric data analyses.
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Punzo A, Bagnato L. The multivariate tail-inflated normal distribution and its application in finance. J STAT COMPUT SIM 2020. [DOI: 10.1080/00949655.2020.1805451] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Antonio Punzo
- Dipartimento di Economia e Impresa, Università degli Studi di Catania, Catania, Italy
| | - Luca Bagnato
- Dipartimento di Scienze Economiche e Sociali, Università Cattolica del Sacro Cuore, Piacenza, Italy
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Auder B, Gassiat E, Loum MA. Least squares moment identification of binary regression mixture models. METRIKA 2020. [DOI: 10.1007/s00184-020-00787-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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11
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Tomarchio SD, Punzo A. Dichotomous unimodal compound models: application to the distribution of insurance losses. J Appl Stat 2020; 47:2328-2353. [DOI: 10.1080/02664763.2020.1789076] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
| | - Antonio Punzo
- Dipartimento di Economia e Impresa, Università degli Studi di Catania, Catania, Italy
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13
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Punzo A, Ingrassia S, Maruotti A. Multivariate hidden Markov regression models: random covariates and heavy-tailed distributions. Stat Pap (Berl) 2019. [DOI: 10.1007/s00362-019-01146-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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14
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Punzo A. A new look at the inverse Gaussian distribution with applications to insurance and economic data. J Appl Stat 2018. [DOI: 10.1080/02664763.2018.1542668] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Antonio Punzo
- Department of Economics and Business, University of Catania, Catania, Italy
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Finite mixture of regression models for censored data based on scale mixtures of normal distributions. ADV DATA ANAL CLASSI 2018. [DOI: 10.1007/s11634-018-0337-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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