{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:50:55Z","timestamp":1747198255913,"version":"3.40.5"},"reference-count":41,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we study linear regression models in which the error term has shape mixtures of skew-normal distribution.\nThis type of distribution belongs to the skew-normal (SN) distribution class that can be used for heavy tails and asymmetry data.\nFor the first time, for the classical (non-Bayesian) estimation of the parameters of the SN family, we apply the Markov chains Monte Carlo ECM (MCMC-ECM) algorithm where the samples are generated by Gibbs sampling, denoted by Gibbs-ECM, and also, we extend two other types of the EM algorithm for the above model.\nFinally, the proposed method is evaluated through a simulation and compared with the Numerical Math-ECM algorithm and Monte Carlo ECM (MC-ECM) using a real data set.<\/jats:p>","DOI":"10.1515\/mcma-2024-2003","type":"journal-article","created":{"date-parts":[[2024,4,10]],"date-time":"2024-04-10T12:11:26Z","timestamp":1712751086000},"page":"137-148","source":"Crossref","is-referenced-by-count":1,"title":["Estimation in shape mixtures of skew-normal linear regression models via ECM coupled with Gibbs sampling"],"prefix":"10.1515","volume":"30","author":[{"given":"Zakaria","family":"Alizadeh Ghajari","sequence":"first","affiliation":[{"name":"Department of Statistics , 201560 Marvdasht Branch, Islamic Azad University , Marvdasht , Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6234-3303","authenticated-orcid":false,"given":"Karim","family":"Zare","sequence":"additional","affiliation":[{"name":"Department of Statistics , 201560 Marvdasht Branch, Islamic Azad University , Marvdasht , Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1983-1491","authenticated-orcid":false,"given":"Soheil","family":"Shokri","sequence":"additional","affiliation":[{"name":"Department of Mathematics , 201524 Rasht Branch, Islamic Azad University , Rasht , Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,4,11]]},"reference":[{"key":"2024052809495388893_j_mcma-2024-2003_ref_001","doi-asserted-by":"crossref","unstructured":"S. Allassonni\u00e8re, E. Kuhn and A. Trouv\u00e9,\nConstruction of Bayesian deformable models via a stochastic approximation algorithm: A convergence study,\nBernoulli 16 (2010), no. 3, 641\u2013678.","DOI":"10.3150\/09-BEJ229"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_002","doi-asserted-by":"crossref","unstructured":"D. F. Andrews and C. L. Mallows,\nScale mixtures of normal distributions,\nJ. Roy. Statist. Soc. Ser. B 36 (1974), 99\u2013102.","DOI":"10.1111\/j.2517-6161.1974.tb00989.x"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_003","doi-asserted-by":"crossref","unstructured":"R. B. Arellano-Valle, R. B. Bolfarine and H. Lachos,\nSkew-normal linear mixed models,\nJ. Data Sci. 3 (2005), 415\u2013438.","DOI":"10.6339\/JDS.2005.03(4).238"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_004","doi-asserted-by":"crossref","unstructured":"R. B. Arellano-Valle, L. M. Castro, M. G. Genton and H. W. G\u00f3mez,\nBayesian inference for shape mixtures of skewed distributions, with application to regression analysis,\nBayesian Anal. 3 (2008), no. 3, 513\u2013539.","DOI":"10.1214\/08-BA320"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_005","doi-asserted-by":"crossref","unstructured":"R. B. Arellano-Valle, C. S. Ferreira and M. G. Genton,\nScale and shape mixtures of multivariate skew-normal distributions,\nJ. Multivariate Anal. 166 (2018), 98\u2013110.","DOI":"10.1016\/j.jmva.2018.02.007"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_006","doi-asserted-by":"crossref","unstructured":"R. B. Arellano-Valle, M. G. Genton and R. H. Loschi,\nShape mixtures of multivariate skew-normal distributions,\nJ. Multivariate Anal. 100 (2009), no. 1, 91\u2013101.","DOI":"10.1016\/j.jmva.2008.03.009"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_007","doi-asserted-by":"crossref","unstructured":"R. B. Arellano-Valle, H. W. G\u00f3mez and F. A. Quintana,\nA new class of skew-normal distributions,\nComm. Statist. Theory Methods 33 (2004), no. 7, 1465\u20131480.","DOI":"10.1081\/STA-120037254"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_008","doi-asserted-by":"crossref","unstructured":"B. C. Arnold and R. J. Beaver,\nThe skew-Cauchy distribution,\nStatist. Probab. Lett. 49 (2000), no. 3, 285\u2013290.","DOI":"10.1016\/S0167-7152(00)00059-6"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_009","unstructured":"A. Azzalini,\nA class of distributions which includes the normal ones,\nScand. J. Statist. 12 (1985), no. 2, 171\u2013178."},{"key":"2024052809495388893_j_mcma-2024-2003_ref_010","doi-asserted-by":"crossref","unstructured":"A. Azzalini and A. Capitanio,\nStatistical applications of the multivariate skew normal distribution,\nJ. R. Stat. Soc. Ser. B Stat. Methodol. 61 (1999), no. 3, 579\u2013602.","DOI":"10.1111\/1467-9868.00194"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_011","doi-asserted-by":"crossref","unstructured":"A. Azzalini, T. Dal Capello and S. Kotz,\nLog-skew-normal and log-skew-t distributions as models for family income data,\nJIncomDistrib. 11 (2003), 13\u201321.","DOI":"10.25071\/1874-6322.1249"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_012","doi-asserted-by":"crossref","unstructured":"A. Azzalini and A. Dalla Valle,\nThe multivariate skew-normal distribution,\nBiometrika 83 (1996), no. 4, 715\u2013726.","DOI":"10.1093\/biomet\/83.4.715"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_013","doi-asserted-by":"crossref","unstructured":"R. M. Basso, V. H. Lachos, C. R. Cabral and P. Ghosh,\nRobust mixture modeling based on scale mixtures of skew-normal distributions,\nComput. Statist. Data Anal. 54 (2010), 2926\u20132941.","DOI":"10.1016\/j.csda.2009.09.031"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_014","doi-asserted-by":"crossref","unstructured":"M. D. Branco and D. K. Dey,\nA general class of multivariate skew-elliptical distributions,\nJ. Multivariate Anal. 79 (2001), no. 1, 99\u2013113.","DOI":"10.1006\/jmva.2000.1960"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_015","doi-asserted-by":"crossref","unstructured":"R. L. Butler, J. B. Mcdonald, R. D. Nelson and S. B. White,\nRobust and partly adaptive estimation of regression models,\nRev. Econ. Statist. 72 (1990), 321\u2013327.","DOI":"10.2307\/2109722"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_016","unstructured":"G. Celeux and J. Diebolt,\nThe SEM algorithm: A probabilistic teacher algorithm derived from the EM algorithm for the mixture problem,\nComput. Statist. Quart. 2 (1985), 73\u201382."},{"key":"2024052809495388893_j_mcma-2024-2003_ref_017","doi-asserted-by":"crossref","unstructured":"K. S. Chan and J. Ledolter,\nMonte Carlo EM estimation for time series models involving counts,\nJ. Amer. Statist. Assoc. 90 (1995), no. 429, 242\u2013252.","DOI":"10.1080\/01621459.1995.10476508"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_018","doi-asserted-by":"crossref","unstructured":"R. D. Cook and S. Weisberg,\nAn Introduction to Regression Graphics,\nWiley Ser. Probab. Stat.,\nJohn Wiley & Sons, New York, 1994.","DOI":"10.1002\/9780470316863"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_019","doi-asserted-by":"crossref","unstructured":"C. da Silva Ferreira, H. Bolfarine and V. H. Lachos,\nSkew scale mixtures of normal distributions: Properties and estimation,\nStat. Methodol. 8 (2011), no. 2, 154\u2013171.","DOI":"10.1016\/j.stamet.2010.09.001"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_020","doi-asserted-by":"crossref","unstructured":"B. Delyon, M. Lavielle and E. Moulines,\nConvergence of a stochastic approximation version of the EM algorithm,\nAnn. Statist. 27 (1999), no. 1, 94\u2013128.","DOI":"10.1214\/aos\/1018031103"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_021","doi-asserted-by":"crossref","unstructured":"A. P. Dempster, N. M. Laird and D. B. Rubin,\nMaximum likelihood from incomplete data via the EM algorithm,\nJ. Roy. Statist. Soc. Ser. B 39 (1977), no. 1, 1\u201338.","DOI":"10.1111\/j.2517-6161.1977.tb01600.x"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_022","doi-asserted-by":"crossref","unstructured":"T. do Bem Mattos, A. M. Garay and V. H. Lachos,\nLikelihood-based inference for censored linear regression models with scale mixtures of skew-normal distributions,\nJ. Appl. Stat. 45 (2018), no. 11, 2039\u20132066.","DOI":"10.1080\/02664763.2017.1408788"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_023","doi-asserted-by":"crossref","unstructured":"C. S. Ferreira, V. H. Lachos and H. Bolfarine,\nInference and diagnostics in skew scale mixtures of normal regression models,\nJ. Stat. Comput. Simul. 85 (2015), no. 3, 517\u2013537.","DOI":"10.1080\/00949655.2013.828057"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_024","doi-asserted-by":"crossref","unstructured":"C. S. Ferreira, V. H. Lachos and H. Bolfarine,\nLikelihood-based inference for multivariate skew scale mixtures of normal distributions,\nAStA Adv. Stat. Anal. 100 (2016), no. 4, 421\u2013441.","DOI":"10.1007\/s10182-016-0266-z"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_025","doi-asserted-by":"crossref","unstructured":"C. E. Galarza, V. H. Lachos and D. Bandyopadhyay,\nQuantile regression in linear mixed models: A stochastic approximation EM approach,\nStat. Interface 10 (2017), no. 3, 471\u2013482.","DOI":"10.4310\/SII.2017.v10.n3.a10"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_026","doi-asserted-by":"crossref","unstructured":"H. W. G\u00f3mez, O. Venegas and H. Bolfarine,\nSkew-symmetric distributions generated by the distribution function of the normal distribution,\nEnvironmetrics 18 (2007), no. 4, 395\u2013407.","DOI":"10.1002\/env.817"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_027","doi-asserted-by":"crossref","unstructured":"W. Jank,\nImplementing and diagnosing the stochastic approximation EM algorithm,\nJ. Comput. Graph. Statist. 15 (2006), no. 4, 803\u2013829.","DOI":"10.1198\/106186006X157469"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_028","doi-asserted-by":"crossref","unstructured":"F. Kahrari, C. S. Ferreira and R. B. Arellano-Valle,\nSkew-normal-Cauchy linear mixed models,\nSankhya B 81 (2019), no. 2, 185\u2013202.","DOI":"10.1007\/s13571-018-0173-2"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_029","doi-asserted-by":"crossref","unstructured":"F. Kahrari, M. Rezaei, F. Yousefzadeh and R. B. Arellano-Valle,\nOn the multivariate skew-normal Cauchy distribution,\nStatist. Probab. Lett. 117 (2016), 80\u201388.","DOI":"10.1016\/j.spl.2016.05.005"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_030","unstructured":"M. Khounsiavash, M. Ganjali and T. Baghfalaki,\nA stochastic version of the EM algorithm to analyze multivariate skew-normal data with missing responses,\nAppl. Appl. Math. 6 (2011), no. 12, 412\u2013427."},{"key":"2024052809495388893_j_mcma-2024-2003_ref_031","doi-asserted-by":"crossref","unstructured":"E. Kuhn and M. Lavielle,\nCoupling a stochastic approximation version of EM with an MCMC procedure,\nESAIM Probab. Stat. 8 (2004), 115\u2013131.","DOI":"10.1051\/ps:2004007"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_032","doi-asserted-by":"crossref","unstructured":"E. Kuhn and M. Lavielle,\nMaximum likelihood estimation in nonlinear mixed effects models,\nComput. Statist. Data Anal. 49 (2005), 1020\u20131038.","DOI":"10.1016\/j.csda.2004.07.002"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_033","doi-asserted-by":"crossref","unstructured":"F. V. Labra, A. M. Garay, V. H. Lachos and E. M. M. Ortega,\nEstimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions,\nJ. Statist. Plann. Inference 142 (2012), no. 7, 2149\u20132165.","DOI":"10.1016\/j.jspi.2012.02.018"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_034","doi-asserted-by":"crossref","unstructured":"V. H. Lachos, H. Bolfarine, R. B. Arellano-Valle and L. C. Montenegro,\nLikelihood-based inference for multivariate skew-normal regression models,\nComm. Statist. Theory Methods 36 (2007), no. 9\u201312, 1769\u20131786.","DOI":"10.1080\/03610920601126241"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_035","unstructured":"T. I. Lin, J. C. Lee and S. Y. Yen,\nFinite mixture modelling using the skew normal distribution,\nStatist. Sinica 17 (2007), no. 3, 909\u2013927."},{"key":"2024052809495388893_j_mcma-2024-2003_ref_036","doi-asserted-by":"crossref","unstructured":"C. Liu and D. B. Rubin,\nThe ECME algorithm; A simple extension of EM and ECM with faster monotone convergence,\nBiometrica 80 (1993), 267\u2013278.","DOI":"10.1093\/biomet\/80.3.543"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_037","doi-asserted-by":"crossref","unstructured":"I. Meilijson,\nA fast improvement to the EM algorithm on its own terms,\nJ. Roy. Statist. Soc. Ser. B 51 (1989), no. 1, 127\u2013138.","DOI":"10.1111\/j.2517-6161.1989.tb01754.x"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_038","doi-asserted-by":"crossref","unstructured":"X.-L. Meng and D. B. Rubin,\nMaximum likelihood estimation via the ECM algorithm: A general framework,\nBiometrika 80 (1993), no. 2, 267\u2013278.","DOI":"10.1093\/biomet\/80.2.267"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_039","doi-asserted-by":"crossref","unstructured":"C. P. Robert and G. Casella,\nIntroducing Monte Carlo Methods with R,\nSpringer, New York, 2010.","DOI":"10.1007\/978-1-4419-1576-4"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_040","doi-asserted-by":"crossref","unstructured":"G. C. G. Wei and M. A. Tanner,\nA Monte Carlo implementation of the EM algorithm and the poor man\u2019s data augmentation algorithm,\nJ. Amer. Statist. Assoc. 85 (1990), 699\u2013704.","DOI":"10.1080\/01621459.1990.10474930"},{"key":"2024052809495388893_j_mcma-2024-2003_ref_041","doi-asserted-by":"crossref","unstructured":"R. Zhou, J. Liu, S. Kumar and D. P. Palomar,\nStudent\u2019s \ud835\udc61 VAR modeling with missing data via stochastic EM and Gibbs sampling,\nIEEE Trans. Signal Process. 68 (2020), 6198\u20136211.","DOI":"10.1109\/TSP.2020.3033378"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2003\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2003\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T09:50:38Z","timestamp":1716889838000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2003\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,11]]},"references-count":41,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,10,24]]},"published-print":{"date-parts":[[2024,6,1]]}},"alternative-id":["10.1515\/mcma-2024-2003"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2024-2003","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"type":"print","value":"0929-9629"},{"type":"electronic","value":"1569-3961"}],"subject":[],"published":{"date-parts":[[2024,4,11]]}}}