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Joint modeling of location and scale parameters of the skew-normal distribution. (English) Zbl 1324.62011
Summary: Joint location and scale models of the skew-normal distribution provide useful extension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.

MSC:
62F10 Point estimation
62H12 Estimation in multivariate analysis
Software:
alr3; GLIM
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References:
[1] M Aitkin. Modelling variance heterogeneity in normal regression using GLIM, Appl Statist, 1987, 36: 332–339. · doi:10.2307/2347792
[2] B C Arnold, R J Beaver. Skewed multivariate models related to hidden truncation and/or selective reporting (with discussion), TEST, 2002, 11: 7–54. · Zbl 1033.62013 · doi:10.1007/BF02595728
[3] A Azzalini. A class of distributions which includes the normal ones, Scand J Statist, 1985, 12: 171–178. · Zbl 0581.62014
[4] A Azzalini, A Capitanio. Statistical applications of the multivariate skew normal distribution, J Roy Statist Soc Ser B, 1999, 61: 579–602. · Zbl 0924.62050 · doi:10.1111/1467-9868.00194
[5] A Azzalini, A Capitanio. Distributions generate by perturbation of symmetry with emphasis on a multivariate skew-t distribution, J Roy Statist Soc Ser B, 2003, 65: 367–389. · Zbl 1065.62094 · doi:10.1111/1467-9868.00391
[6] V G Cancho, V H Lachos, E M Ortega. A nonlinear regression model with skew-normal errors, Statist Papers, 2010, 51: 547–558. · Zbl 1247.62160 · doi:10.1007/s00362-008-0139-y
[7] J Engel, A F Huele. A generalized linear modeling approach to robust design, Technometrics, 1996, 38: 365–373. · Zbl 0896.62071 · doi:10.1080/00401706.1996.10484548
[8] A K Gupta, T Chen. Goodness of fit tests for the skew-normal distribution, Comm Statist Simulation Comput, 2001, 30: 907–930. · Zbl 1008.62590 · doi:10.1081/SAC-100001854
[9] R D Gupta, R C Gupta. Analyzing skewed data by power normal model, TEST, 2008, 17: 197–210. · Zbl 1148.62008 · doi:10.1007/s11749-006-0030-x
[10] A C Harvey. Estimating regression models with multiplicative heteroscedasticity, Econometrica, 1976, 44: 460–465. · Zbl 0333.62040 · doi:10.2307/1913974
[11] J G Lin, F C Xie and B C Wei. Statistical diagnostics for skew-t-normal nonlinear models, Comm Statist Simulation Comput, 2009, 38: 2096–2110. · Zbl 1182.62150 · doi:10.1080/03610910903249502
[12] T I Lin, J C Lee and S Y Yen. Finite mixture modelling using the skew normal distribution, Statist Sinica, 2007, 17: 909–927. · Zbl 1133.62012
[13] T I Lin, Y J Wang. Bayesian inference in joint modelling of location and scale parameters of the t distribution for longitudinal data, J Statist Plann Inference, 2010, 141: 1543–1553. · Zbl 1204.62040 · doi:10.1016/j.jspi.2010.11.001
[14] T I Lin, Y J Wang. A robust approach to joint modeling of mean and scale covariance for longitudinal data, J Statist Plann Inference, 2009, 139: 3013–3026. · Zbl 1168.62082 · doi:10.1016/j.jspi.2009.02.008
[15] R E Park. Estimation with heteroscedastic error terms, Econometrica, 1966, 34: 888. · doi:10.2307/1910108
[16] J T Taylor, A P Verbyla. Joint modelling of location and scale parameters of the t distribution, Stat Model, 2004, 4: 91–112. · Zbl 1112.62010 · doi:10.1191/1471082X04st068oa
[17] A P Verbyla. Variance heterogeneity: residual maximum likelihood and diagnostics, J Roy Statist Soc Ser B, 1993, 52: 493–508. · Zbl 0783.62051
[18] S Weisberg. Applied Linear Regression, Wiley, New York, 1985. · Zbl 0646.62058
[19] L C Wu, H Q Li. Variable selection for joint mean and dispersion models of the inverse Gaussian distribution, Metrika, 2012, 75: 795–808. · Zbl 1410.62132 · doi:10.1007/s00184-011-0352-x
[20] F C Xie, J G Lin and B C Wei. Diagnostics for skew-normal nonlinear regression models with AR(1) errors, Comput Statist Data Anal, 2009, 53: 4403–4416. · Zbl 05689188 · doi:10.1016/j.csda.2009.06.010
[21] F C Xie, B C Wei and J G Lin. Homogeneity diagnostics for skew-normal nonlinear regression models, Statist Probab Lett, 2009, 79: 821–827. · Zbl 1157.62044 · doi:10.1016/j.spl.2008.11.001
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