Variable Selection for Joint Mean and Dispersion Models of the Lognormal Distribution

Year 2012, Volume: 41 Issue: 2, 307 - 320, 01.02.2012

L.-c. Wu Z.-z. Zhang D.-k. Xu

Keywords

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References

• Aitkin , M. Modelling variance heterogeneity in normal regression using GLIM, Applied Statistics 36, 332–339, 1987.
• Antoniadis, A. Wavelets in statistics: a review (with discussion), Journal of the Italian Statistical Association 6, 97–144, 1997.
• Carroll, R. J. The effect of variance function estimating on prediction and calibration: an example, In Statistical Decision Theory and Related Topics IV (eds J. O. Berger and S. S.Gupta) vol.II. (Springer, Heidelberg, 1987).
• Carroll, R. J. and Rupert, D. Transforming and weighting in regression (Chapman and Hall, London, 1988).
• Crow, E. and Shimizu, K. Lognormal distributions: theory and practice (Marcel Decker, New York, 1988).
• Fan, J. Q. and Li, R. Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of American Statistical Association 96, 1348–1360, 2001.
• Fan, J. Q. and Lv, J. C. A selective overview of variable selection in high dimensional feature space, Statistica Sinica 20, 101–148, 2010.
• Harvey, A. C. Estimating regression models with multiplicative heteroscedasticity, Econo- metrica 44, 460–465, 1976.
• Lee, Y. and Nelder, J. A. Generalized linear models for the analysis of quality improvement experiments, The Canadian Journal of Statistics 26 (1), 95–105, 1998.
• Li, G. R., Peng, H. and Zhu, L. X. Nonconcave penalized M-estimation with a diverging number of parameters, Statistica Sinica 21, 391–419, 2011.
• Li, R. and Liang, H. Variable selection in semiparametric regression modeling, The Annals of Statistics 36, 261–286, 2008.
• Limpert, E., Stahel, W. A. and Abbt, M. Lognormal distributions across the sciences: Keys and clues, BioScience 51, 341–352, 2001.
• Nelder, J. A. and Lee, Y. Generalized linear models for the analysis of Taguchi-type exper- iments, Applied Stochastic Models and Data Analysis 7, 107–120, 1991.
• Park, R. E. Estimation with heteroscedastic error terms, Econometrica 34, 888, 1966.
• Shimizu, K. et.al. Lognormal distribution and its applications (John Wiley and Sons, New York, 1988).
• Smyth, G. K. Generalized linear models with varying dispersion, Journal of the Royal Sta- tistical Society, Series B 51, 47–60, 1989.
• Smyth, G. K. and Verbyla, A. P. Adjusted likelihood methods for modelling dispersion in generalized linear models, Environmetrics 10, 696–709, 1999.
• Taylor, J. T. and Verbyla, A. P. Joint modelling of location and scale parameters of the t distribution, Statistical Modelling 4, 91–112, 2004.
• Tibshirani, R. Regression shrinkage and selection via the LASSO, Journal of the Royal Statistical Society, Series B 58, 267–288, 1996.
• Verbyla, A. P. Variance heterogeneity: residual maximum likelihood and diagnostics, Journal of the Royal Statistical Society, Series B 52, 493–508, 1993.
• Wang, D. R. and Zhang, Z. Z. Variable selection in joint generalized linear models, Chinese Journal of Applied Probability and Statistics 25, 245–256, 2009.
• Wang, H., Li, R. and Tsai, C. Tuning parameter selectors for the smoothly clipped absolute deviation method, Biometrika 94, 553–568, 2007.
• Weisberg, S. Applied Linear Regression (Wiley, New York, 1985).
• Zhao, P. X. and Xue, L. G. Variable selection for semiparametric varying coefficient partially linear errors-in-variables models, Journal of Multivariate Analysis 101, 1872–1883, 2010.