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Original Articles

Likelihood-based inference for censored linear regression models with scale mixtures of skew-normal distributions

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Pages 2039-2066 | Received 27 Nov 2016, Accepted 19 Nov 2017, Published online: 02 Dec 2017

References

  • H. Akaike, A new look at the statistical model identification, IEEE Trans. Autom. Cont. 19 (1974), pp. 716–723. doi: 10.1109/TAC.1974.1100705
  • D.F. Andrews and C.L. Mallows, Scale mixtures of normal distributions, J. R. Stat. Soc. Series B 36 (1974), pp. 99–102.
  • R.B. Arellano-Valle, L.M. Castro, G. González-Farías, and K.A. Muñoz-Gajardo, Student-t censored regression model: properties and inference, Stat. Methods. Appt. 21 (2012), pp. 453–473. doi: 10.1007/s10260-012-0199-y
  • A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Stat. 12 (1985), pp. 171–178.
  • Z.D. Bai, P.R. Krishnaiah, and L.C. Zhao, On rates of convergence of efficient detection criteria in signal processing with white noise, IEEE Trans. Inf. Theory 35 (1989), pp. 380–388. doi: 10.1109/18.32132
  • M. Barros, M. Galea, M. González, and V. Leiva, Influence diagnostics in the Tobit censored response model, Stat. Methods Appl. 19 (2010), pp. 716–723. doi: 10.1007/s10260-010-0135-y
  • R..M. Basso, V.H. Lachos, C.R. Cabral, and P. Ghosh, Robust mixture modeling based on scale mixtures of skew-normal distributions, Comput. Stat. Data Anal. 54 (2010), pp. 2926–2941. doi: 10.1016/j.csda.2009.09.031
  • M.D. Branco and D.K. Dey, A general class of multivariate skew-elliptical distributions, J. Multivariate Anal. 79 (2001), pp. 99–113. doi: 10.1006/jmva.2000.1960
  • M. Buchinsky and J. Hahn, An alternative estimator for the censored quantile regression model, Econometrica 66 (1998), pp. 653–671. doi: 10.2307/2998578
  • C.R.B. Cabral, V.H. Lachos, and M.R. Madruga, Bayesian analysis of skew-normal independent linear mixed models with heterogeneity in the random-effects population, J. Stat. Plan. Inference. 142 (2012), pp. 181–200. doi: 10.1016/j.jspi.2011.07.007
  • V.G. Cancho, D.K. Dey, V.H. Lachos, and M.G. Andrade, Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics, Comput. Stat. Data Anal. 55 (2011), pp. 588–602. doi: 10.1016/j.csda.2010.05.032
  • C. Couvreur, The EM algorithm: A guided tour, in Proceedings of the 2d IIEE European Workshop on Computationally Intensive Methods in Control and Signal Processing, Prague, Czech Republic, 1996.
  • B. Delyon, M. Lavielle, and E. Moulines, Convergence of a stochastic approximation version of the EM algorithm, Ann. Stat. 27 (1999), pp. 94–128. doi: 10.1214/aos/1018031103
  • A. Dempster, N. Laird, and D. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B 39 (1977), pp. 1–38.
  • E.D. Feigelson, Censoring in astronomical data due to nondetections, in Statistical Challenges in Modern Astronomy, E. D. Feigelson, G. J. Babu, eds., Springer, New York, 1992, pp. 221–237.
  • E.D. Feigelson, astrodatR: Astronomical Data (2014). Available at https://cran.r-project.org/web/packages/astrodatR/, R package v. 0.1.
  • C. Fernández and M.J.F. Steel, Multivariate Student-t regression models: Pitfalls and inference, Biometrika 86 (1999), pp. 153–167. doi: 10.1093/biomet/86.1.153
  • B. Fitzenberger, 15 a guide to censored quantile regressions, Handbook Stat. 15 (1997), pp. 405–437. doi: 10.1016/S0169-7161(97)15017-9
  • C.E. Galarza, V.H. Lachos, and D. Bandyopadhyay, Quantile regression for linear mixed models: A stochastic approximation EM approach, Stat. Interface. 10 (2017), pp. 471–482. doi: 10.4310/SII.2017.v10.n3.a10
  • A.M. Garay, L.M. Castro, J. Leskow, and V.H. Lachos, Censored linear regression models for irregularly observed longitudinal data using the multivariate-t distribution, Stat. Methods. Med. Res. 26 (2017), pp. 542–566. doi: 10.1177/0962280214551191
  • A.M. Garay, V.H. Lachos, and C.A. Abanto-Valle, Nonlinear regression models based on scale mixtures of skew-normal distributions, J. Korean. Stat. Soc. 40 (2011), pp. 115–124. doi: 10.1016/j.jkss.2010.08.003
  • A.M. Garay, V.H. Lachos, H. Bolfarine, and C.R.B. Cabral, Linear censored regression models with scale mixtures of normal distributions, Stat. Pap. 58 (2017), pp. 247–278. doi: 10.1007/s00362-015-0696-9
  • G. Ibacache-Pulgar and G.A. Paula, Local influence for Student-t partially linear models, Comput. Stat. Data. Anal. 55 (2011), pp. 1462–1478. doi: 10.1016/j.csda.2010.10.009
  • W. Jank, Implementing and diagnosing the stochastic approximation EM algorithm, J. Comput. Graph. Stat. 15 (2006), pp. 803–829. doi: 10.1198/106186006X157469
  • E. Kuhn and M. Lavielle, Coupling a stochastic approximation version of EM with an MCMC procedure, ESAIM Probab. Stat. 8 (2004), pp. 115–131. doi: 10.1051/ps:2004007
  • F.V. Labra, A.M. Garay, V.H. Lachos, and E.M.M. Ortega, Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions, J. Stat. Plan. Inference. 142 (2012), pp. 2149–2165. doi: 10.1016/j.jspi.2012.02.018
  • V.H. Lachos, P. Ghosh, and R.B. Arellano-Valle, Likelihood based inference for skew–normal independent linear mixed models, Stat. Sin. 20 (2010), pp. 303–322.
  • K.L. Lange and J.S. Sinsheimer, Normal/independent distributions and their applications in robust regression, J. Comput. Graph. Stat. 2 (1993), pp. 175–198.
  • T.I. Lin, Robust mixture modeling using multivariate skew-t distributions, Stat. Comput. 20 (2010), pp. 343–356. doi: 10.1007/s11222-009-9128-9
  • T.A. Louis, Finding the observed information matrix when using the EM algorithm, J. R. Stat. Soc. Ser. B 44 (1982), pp. 226–233.
  • M.B. Massuia, C.R.B. Cabral, L.A. Matos, and V.H. Lachos, Influence diagnostics for Student-t censored linear regression models, Statistics 49 (2015), pp. 1074–1094. doi: 10.1080/02331888.2014.958489
  • M.B. Massuia, A.M. Garay, V.H. Lachos, and C.R.B. Cabral, Bayesian analysis of censored linear regression models with scale mixtures of skew-normal distributions, Stat. Interface 10 (2017), pp. 425–439. doi: 10.4310/SII.2017.v10.n3.a7
  • G. McLachlan and D. Peel, Finite Mixture Models, Wiley Series in Probability and Statistics, Wiley, New York, NY, 2000.
  • I. Meilijson, A fast improvement to the EM algorithm to its own terms., J. R. Stat. Soc. Ser. B 51 (1989), pp. 127–138.
  • C. Meza, F. Osorio, and R. De la Cruz, Estimation in nonlinear mixed-effects models using heavy-tailed distributions, Stat. Comput. 22 (2012), pp. 121–139. doi: 10.1007/s11222-010-9212-1
  • T.A. Mroz, The sensitivity of an empirical model of married women's hours of work to economic and statistical assumptions, Econometrica 55 (1987), pp. 765–799. doi: 10.2307/1911029
  • E.M.M. Ortega, H. Bolfarine, and G.A. Paula, Influence diagnostics in generalized log-gamma regression models, Comput. Stat. Data Anal. 42 (2003), pp. 165–186. doi: 10.1016/S0167-9473(02)00104-4
  • J.L. Powell, Least absolute deviations estimation for the censored regression model, J. Econom. 25 (1984), pp. 303–325. doi: 10.1016/0304-4076(84)90004-6
  • J.L. Powell, Censored regression quantiles, J. Econom. 32 (1986), pp. 143–155. doi: 10.1016/0304-4076(86)90016-3
  • R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2015). Available at http://www.R-project.org, ISBN 3-900051-07-0.
  • D.B. Rubin, The calculation of posterior distributions by data augmentation: Comment: A noniterative sampling/importance resampling alternative to the data augmentation algorithm for creating a few imputations when fractions of missing information are modest: The SIR algorithm, J. Am. Stat. Assoc. 82 (1987), pp. 543–546.
  • D.B. Rubin, Using the SIR algorithm to simulate posterior distributions, Bayesian Stat. 3 (1988), pp. 395–402.
  • N. Santos, R.G. López, G. Israelian, M. Mayor, R. Rebolo, A. García-Gil, M.P. de Taoro, and S. Randich, Beryllium abundances in stars hosting giant planets, Astron. Astrophys 386 (2002), pp. 1028–1038. doi: 10.1051/0004-6361:20020280
  • G. Schwarz, Estimating the dimension of a model, Ann. Stat. 6 (1978), pp. 461–464. doi: 10.1214/aos/1176344136
  • J. Tobin, Estimation of relationships for limited dependent variables, Econometrica: J. Econom. Soc. 26 (1958), pp. 24–36. doi: 10.2307/1907382
  • F. Vaida, Parameter convergence for EM and MM algorithms, Stat. Sin. 15 (2005), pp. 831–840.
  • G.C. Wei and M.A. Tanner, A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms, J. Am. Stat. Assoc. 85 (1990), pp. 699–704. doi: 10.1080/01621459.1990.10474930
  • C.J. Wu, On the convergence properties of the EM algorithm, Ann. Stat. 11 (1983), pp. 95–103. doi: 10.1214/aos/1176346060

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