Abstract
In this paper, the class of multivariate skew slash distributions under different type of setting is introduced and its density function is discussed. A procedure to obtain the Maximum Likelihood estimators for this family is studied. In addition, the Maximum Likelihood estimators for the mixture model based on this family are discussed. For illustration of the main results, we use the actual data coming from the Inner Mongolia Academy of Agriculture and Animal Husbandry Research Station to show the performance of the proposed algorithm.
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References
Andrews DF, Bickel PJ, Hampel FR, Huber PJ, Rogers WH, Tukey JW (1972) Robust estimates of location: survey and advances. Princeton University Press, Princeton
Arellano-Valle RB, Bolfarine H, Lachos VH (1907) Bayesian inference for skew normal linear mixed models. J Appl Stat 34(6):663–682
Arellano-Valle R, Ozan S, Bolfarine H, Lachos V (2005) Skew normal measurement error models. J Multivar Anal 96(2):265–281
Arslan O (2008) An alternative multivariate skew slash distribution. Stat Prob Lett 78(16):2756–2761
Arslan O (2009) Maximum likelihood parameter estimation for the multivariate skew slash distribution. Stat Prob Lett 79(20):2158–2165
Arslan O, Genc AI (2009) A generalization of the multivariate slash distribution. J Stat Plan Inf 139(3):1164–1170
Azzalini A (1985) A class of distributions which includes the normal ones. Scandinavian J Stat 12(2):171–178
Azzalini A, Capitanio A (1999) Statistical applications of the multivariate skew normal distribution. J R Stat Soc Ser B (Stat Methodol) 61(3):579–602
Azzalini A, Dalla Valle A (1996) The multivariate skew normal distribution. Biometrika 83(4):715–726
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B (Methodological) 39(1):1–38
Gomez HW, Quintana FA, Torres FJ (2007) A new family of slash-distributions with elliptical contours. Stat Prob Lett 77(7):717–725
Gross AM (1973) A Monte Carlo swindle for estimators of location. Appl Stat 22:347–353
Gupta A, Huang W (2002) Quadratic forms in skew normal variates. J Math Anal Appl 273(2):558–564
Lin TI (2009) Maximum likelihood estimation for multivariate skew normal mixture models. J Multivar Anal 100(2):257–265
MacKenzie G, Peng D (2014) Introduction. Springer International Publishing, Switzerland, pp 1–6
Morgenthaler S, Tukey JW (1991) Configural polysampling: a route to practical robustness. Wiley, NewYork
Reyes J, Gmez HW, Bolfarine H (2013) Modified slash distribution. Statistics 47(5):929–941
Rogers WH, Tukey JW (1972) Understanding some long-tailed symmetrical distributions. Statistica Neerlandica 26(3):211–226
Sahu SK, Dey DK, Branco MD (2003) A new class of multivariate skew distributions with applications to Bayesian regression models. Can J Stat 31(2):129–150
Sekely G, Rizzo M (2005) A new test for multivariate normality. J Multivar Anal 93(1):58–80
Wang J, Genton MG (2006) The multivariate skew slash distribution. J Stat Plan Inf 136(1):209–220
Acknowledgements
This material is based upon work funded by National Natural Science Foundation of China (Grant No. IRT1259).
We gratefully acknowledge referees for their valuable comments and suggestions which greatly improve this paper.
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Tian, W., Han, G., Wang, T., Pipitpojanakarn, V. (2017). EM Estimation for Multivariate Skew Slash Distribution. In: Kreinovich, V., Sriboonchitta, S., Huynh, VN. (eds) Robustness in Econometrics. Studies in Computational Intelligence, vol 692. Springer, Cham. https://doi.org/10.1007/978-3-319-50742-2_14
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DOI: https://doi.org/10.1007/978-3-319-50742-2_14
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