273
Views
35
CrossRef citations to date
0
Altmetric
Original Articles

Maximum a-posteriori estimation of autoregressive processes based on finite mixtures of scale-mixtures of skew-normal distributions

&
Pages 1061-1083 | Received 15 Jul 2016, Accepted 03 Oct 2016, Published online: 26 Oct 2016

References

  • Böhning D. Computer-assisted analysis of mixtures and applications. Meta-analysis, disease mapping and others. Boca Raton, FL: Chapman & Hall/CRC; 2000.
  • McLachlan GJ, Peel D. Finite mixture models. Chichester: Wiley; 2000.
  • Frühwirth-Schnatter S. Finite mixture and Markov switching models. Springer series in statistics. New York: Springer; 2006.
  • Mengersen K, Robert C, Titterington D. Mixtures: estimation and applications. Chichester: Wiley; 2011.
  • Punzo A, McNicholas PD. Parsimonious mixtures of multivariate contaminated normal distributions. Biometr J. To appear; 2016.
  • Andrews DR, Mallows CL. Scale mixture of normal distributions. J R Statist Soc Ser B. 1974;36:99–102.
  • Lin TI, Lee JC, Yen SY. Finite mixture modeling using the skew-normal distribution. Statist Sin. 2007;17(b):909–927.
  • Branco, MD, Dey, DK. A general class of multivariate skew-elliptical distributions. J Multivariate Anal. 2001;79:99–113. doi:10.1006/jmva.2000.1960
  • Lin TI. Maximum likelihood estimation for multivariate skew normal mixture models. J Multivariate Anal. 2009;100(2):257–265. doi:10.1016/j.jmva.2008.04.010
  • Lin TI. Robust mixture modeling using multivariate skew t distributions. Stat Comput. 2010;20(3):343–356. doi:10.1007/s11222-009-9128-9
  • Lee SX, McLachlan GJ. Model-based clustering and classification with non-normal mixture distributions. Statist Methods Appl. 2013;22(4):427–454. doi:10.1007/s10260-013-0237-4
  • Lee SX, McLachlan GJ. On mixtures of skew normal and skew t distributions. Adv Data Anal Classif. 2013;7(3):241–266. doi:10.1007/s11634-013-0132-8
  • Azzalini A. with the collaboration of Capitanio A. The skew-normal and related families. Cambridge: Cambridge University Press; 2014. IMS Monographs series.
  • Genton MG. Skew-elliptical distributions and their applications: a journey beyond normality. Boca Raton, FL: Chapman & Hall/CRC; 2004. Edited Volume. doi:10.1201/9780203492000
  • Arellano-Valle RB, Genton MG. On fundamental skew distributions. J Multivariate Anal. 2005;96:93–116. doi:10.1016/j.jmva.2004.10.002
  • Arellano-Valle RB, Azzalini A. On unification of skew normal families. Scand J Stat. 2006;33:561–574. doi:10.1111/j.1467-9469.2006.00503.x
  • Arellano-Valle RB, Branco MD, Genton MG. A unified view on skewed distributions arising from selections. Canad J Stat. 2006;34:561–574. doi:10.1111/j.1467-9469.2006.00503.x
  • Basso RM, Lachos VH, Cabral CRB, Ghosh P. Robust mixture modeling based on the scale mixtures of skew-normal distributions. Comput Stat Data Anal. 2010;54:2926–2941. doi:10.1016/j.csda.2009.09.031
  • Pyne S, Hu X, Wang K, Rossin E, Lin TI, Maier LM, Baecher-Allan C, McLachlan GJ, Tamayo P, Hafler DA, De Jager PL, Mesirow JP. Automated high-dimensional flow cytometric data analysis. Proc Natl Acad Sci USA. 2009;106:8519–8524. doi:10.1073/pnas.0903028106
  • Frühwirth-Schnatter S, Pyne S. Bayesian inference for finite mixtures of univariate and multivariate skew-normal and skew-t distributions. Biostatistics. 2010;11(2):317–336. doi:10.1093/biostatistics/kxp062
  • Franczak BC, Browne RP, McNicholas PD. Mixtures of shifted asymmetric Laplace distributions. IEEE Trans Pattern Anal. 2014;36(6):1149–1157. doi:10.1109/TPAMI.2013.216
  • Wang K., Ng SK, McLachlan GJ. Multivariate skew t mixture models: Applications to fluorescence-activated cell sorting data. In: Shi H, Zhang Y, Bottema MJ, et al., editors. Proceedings of conference of digital image computing: techniques and applications. Los Alamitos, CA: IEEE; 2009. p. 526–531
  • Lee SX, McLachlan GJ. Finite mixtures of multivariate skew t distributions: some recent and new results. Stat Comput. 2014;24:181–202. doi:10.1007/s11222-012-9362-4
  • Vrbik I, McNicholas PD. Analytic calculations for the EM algorithm for multivariate skew-t mixture models. Stat Probabil Lett. 2012;82(6):1169–1174. doi:10.1016/j.spl.2012.02.020
  • Karlis D, Santourian A. Model-based clustering with non-elliptically con-toured distributions. Stat Comput. 2009;19(1):73–83. doi:10.1007/s11222-008-9072-0
  • Morris K, McNicholas P, Punzo A, Browne RP. Robust asymmetric clustering. arXiv.org e-print 1402.6744. 2014; available at: http://arxiv.org/abs/1402.6744
  • Browne RP, McNicholas PD. A mixture of generalized hyperbolic distributions. Canad J Stat. 2015;43(2):176–198. doi:10.1002/cjs.11246
  • Li WK, Mcleod AI. ARMA modeling with non-Gaussian innovations. J Time Ser Anal. 1988;9:155–168. doi:10.1111/j.1467-9892.1988.tb00461.x
  • Andel J. On AR(1) processes with exponential white noise. Commun Stat – Theory Method. 1988;17:1481–1495. doi:10.1080/03610928808829693
  • Janacek GJ, Swift AL. A class of models for non-normal time series. J Time Ser Anal. 1990;11:19–31. doi:10.1111/j.1467-9892.1990.tb00039.x
  • Zellner A. Bayesian and non-Bayesian analysis of the regression model with multivariate student-t error terms. J Am Stat Assoc. 1976;71:400–405.
  • Lange KL, Little RJA, Taylor JMG. Robust statistical modeling using the t-distribution. J Am Stat Assoc. 1989;84:881–896.
  • Tiku ML, Wong WK, Vaughan DC, Bian G. Time series models in non-normal situations; Symmetric innovations. J Time Ser Anal. 2000;21:571–596. doi:10.1111/1467-9892.00199
  • Penny WD, Roberts SJ. Variational Bayes for generalized autoregressive models. IEEE Transm Signal Process. 2002;50(9):2245–2257. doi:10.1109/TSP.2002.801921
  • Christmas J, Everson R. Robust autoregression: Student-t innovations using variational Bayes. IEEE Transm Signal Process. 2011;59:48–57. doi:10.1109/TSP.2010.2080271
  • Azzalini A. A class of distributions which includes the normal ones. Scandi J Stat. 1985;12:171–178.
  • Pourahmadi M. Skew-normal ARMA models with nonlinear heteroscedastic predictors. Commun Stat Theory Methods. 2007;36:1803–1819. doi:10.1080/03610920601126274
  • Azzalini A, Dalla Valle A. The multivariate skew-normal distribution. Biometrika. 1996;83:715–726. doi:10.1093/biomet/83.4.715
  • Azzalini A, Capitanio A. Statistical applications of the multivariate skew-normal distribution. J R Stat Soc Ser B. 1999;61:579–602. doi:10.1111/1467-9868.00194
  • Minozzo M, Ferracuti L. On the existence of some skew-normal stationary processes. Chilean J Stat. 2012;3(2):157–170.
  • Bondon P. Estimation of autoregressive models with epsilon-skew-normal innovations. J Multivariate Anal. 2009;100:1761–1776. doi:10.1016/j.jmva.2009.02.006
  • Mudholkar GS, Hutson AD. The epsilon-skew-normal distribution for analyzing near-normal data. J Stat Plan Inference. 2000;83:291–309. doi:10.1016/S0378-3758(99)00096-8
  • Hutson A. Utilizing the flexibility of the epsilon-skew-normal distribution for common regression. J Appl Stat. 2004;31(6):673–683. doi:10.1080/1478881042000214659
  • Maleki M, Nematollahi AR. Bayesian approach to epsilon-skew-normal family. Commun Stat Theor Methods. 2016; Just accepted.
  • Contreras-Reyes JE. Analyzing fish condition factor index through skew-gaussian information theory quantifiers. Fluctuat Noise Lett. 2016;15(2):1650013. doi:10.1142/S0219477516500139
  • Arellano-Valle RB, Bolfarine H, Lachos VH. Skew-normal linear mixed models. J Data Sci. 2005;3:415–438.
  • Arellano-Valle RB, Ozan S, Bolfarine H, Lachos VH. Skew normal measurement error models. J Multivariate Anal. 2005;96:265–281. doi:10.1016/j.jmva.2004.11.002
  • Arellano-Valle RB, Castro LM, Genton MG, Gómez HW. Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis. Bayesian Anal. 2008;3(3):513–539.
  • Lachos VH, Ghosh P, Arellano-Valle RB. Likelihood based inference for skew-normal/independent linear mixed models. Statist Sin. 2010a;20:303–322.
  • Zeller CB, Cabral CRB, Lachos VH. Robust mixture regression modeling based on scale mixtures of skew-normal distributions. Comput Stat Data Anal. 2010;54:2926–2941. doi:10.1016/j.csda.2009.11.008
  • Zeller CB, Lachos VH, Vilca-Labra FE. Local influence analysis for regression models with scale mixtures of skew-normal distributions. J Appl Stat. 2011;38:348–363. doi:10.1080/02664760903406504
  • Cancho VG, Dey, DK, Lachos VH, Andrade MG. Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics. Comput Stat Data Anal. 2011;55:588–602. doi:10.1016/j.csda.2010.05.032
  • Garay AM, Lachos VH, Abanto-Valle CA. Nonlinear regression models based on scale mixtures of skew-normal distributions. J Korean Statist Soc. 2011;40:115–124. doi:10.1016/j.jkss.2010.08.003
  • Cabral CRB, Lachos VH, Prates MO. Multivariate mixture modeling using skew-normal independent distributions. Comput Stat Data Anal. 2012;56:126–142. doi:10.1016/j.csda.2011.06.026
  • Lachos VH, Labra FV, Bolfarine H, Ghosh P. Multivariate measurement error models based on scale mixtures of the skew-normal distribution. Statistics. 2010b;44:541–556. doi:10.1080/02331880903236926
  • Labra FV, Garay AM, Lachos VH, Ortega EMM. Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions. J Statist Plan Inference. 2012;142(7):2149–2165. doi:10.1016/j.jspi.2012.02.018
  • Contreras-Reyes JE, Arellano-Valle RB. Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions. Fish Res. 2013;147:137–144. doi:10.1016/j.fishres.2013.05.002
  • Contreras-Reyes JE, Palma W. Statistical analysis of autoregressive fractionally integrated moving average models in R. Comput Stat. 2013;28(5):2309–2331. doi:10.1007/s00180-013-0408-7
  • Contreras-Reyes JE, Arellano-Valle RB, Canales TM. Comparing growth curves with asymmetric heavy-tailed errors: application to the southern blue whiting (Micromesistius australis). Fish Res. 2014;159:88–94. doi:10.1016/j.fishres.2014.05.006
  • Garay AM, Lachos VH, Labra FV, Ortega EMM. Statistical diagnostics for nonlinear regression models based on scale mixtures of skew-normal distributions. J Stat Comput Simul. 2014;84:1761–1778. doi:10.1080/00949655.2013.766188
  • Gauvain JL, Lee CH. Maximun a posteriori estimation for multivariate Gaussian mixture observations of Markov chain. IEEE Tran Trans Speech Audio Process 1994;2(2):291–298. doi:10.1109/89.279278
  • Tolpin D, Wood F. Maximun a posteriori estimation by search in probabilistic programs. In Proceedings of the Eighth Annual Symposium on Combinatorial Search; 2015:201–205.
  • Henze N. A probabilistic representation of the skew-normal distribution. Scandi J Stat. 1986;13:271–275.
  • Azzalini A, Genton M. Robust likelihood methods based on the skew-t and related distributions. Int Stat Rev. 2008;76:1490–1507. doi:10.1111/j.1751-5823.2007.00016.x
  • Arellano-Valle RB, Contreras-Reyes JE, Genton MG. Shannon entropy and mutual information for multivariate skew-elliptical distributions. Scand J Stat. 2013;40:42–46. doi:10.1111/j.1467-9469.2011.00774.x
  • Ó’Ruanaidh JJK, Fitzgerald W. Numerical Bayesian methods applied to signal processing. New York: Springer; 1996.
  • Liu CH, Rubin DB. The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence. Biometrika. 1994;81:633–648. doi:10.1093/biomet/81.4.633
  • Liu CH, Rubin DB. ML estimation of the t distribution using EM and its extensions, ECM and ECME. Statist Sinica. 1995;5:19–40.
  • Wei GCG, Tanner MA. A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithms. J Am Stat Assoc. 1990;85:699–704. doi:10.1080/01621459.1990.10474930
  • McLachlan GJ, Krishnan T. The EM algorithm and extensions. NJ: Wiley; 2008.
  • Prates M, Lachos V, Cabral C. Mixsmsn: Fitting finite mixture of scale mixture of skew-normal distributions. R package version 0.3-2; 2011. Available at http://CRAN.R-project.org/package=mixsmsn
  • Akaike H. A new look at the statistical model identification. IEEE Trans Automat Control. 1974;19:716–723. doi:10.1109/TAC.1974.1100705
  • Schwarz G. Estimating the dimension of a model. Ann Stat. 1978;6:461–464. doi:10.1214/aos/1176344136
  • Brockwell PJ, Davis RA. Time series: theory and methods. 2nd ed. New York: Springer-Verlag; 1991.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.