On Robust Regression: A Model with Weibull Error Term
DOI:
https://doi.org/10.62054/ijdm/0203.17Abstract
A regression model based on the Weibull error distribution has been developed to address the challenges of modeling skewed response variables commonly encountered in environmental and life sciences data. By introducing a location parameter to the standard Weibull distribution, the model accommodates asymmetry and heavy tails that linear normal-based regression often fails to capture. Parameter estimation was carried out using the Newton–Raphson algorithm, implemented in the R program WeiReg. Model comparison based on the Akaike Information Criterion (AIC) demonstrates that the Weibull regression provides a substantially better fit than the linear regression model when applied to wind speed data from Christmas Island, Australia. These findings highlight the relevance of flexible error structures in regression modeling and underscore the practical value of the Weibull approach for analyzing environmental data.
Riferimenti bibliografici
Aldrich, J. (2005). Fisher and Regression, Statistical Science, vol. 20, No 4, 401 – 417, https://DOI:10.1214/08834230500000331 © Institute of Mathematical Statistics
Baissa, D. K. and Rainey, C. When BLUE is not best: Non-normal errors and the linear models. Political Science Research and Methods, (2020), 8, 136 –148. https://doi:10.1017/psrm.2018.34
Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Springer.
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer.
Dielman, T. E. (2009). Least Absolute Value verse Least Squares Estimation and Inference Procedures in Regression Models with Asymmetric Error Distributions, Journal of Modern Applied Statistical Methods, vol. 8, Issue 1, Article 13, pp 147 – 160 @ http://digitalcommons.wayne.edu/jmasm/vol8iss1/13
Ganguly, S. S. (2014). Robust Regression Analysis for Non-Normal Situations Under Symmetric Distributions Arising in Medical Research, Journal of Modern Applied Statistical Methods, vol. 13, Issue 1, Article 29, @ http://digitalcommons.wayne.edu/jmasm/vol13iss1/29
Gongsin I. E. and Saporu F. W. O. (2020) A bivariate conditional Weibull distribution with application, Afrika Matematika, 31:565–583. https://doi.org/10.1007/s13370-019-00742-8
Gujarati, D. N., Porter, D. C. and Gunasekar, S. (2012). Basic Econometrics, Fifth Edition, Tata McGraw Hill Education Private Limited, New Delhi.
Huber, P. J. (1981). Robust Statistics, John Wiley, New York.
Lindsey, K. J. (1997). Applying Generalized Linear Models, © 1997 Springer-Verlag, New York, Inc.
Manning, W. G., Basu, A, and Mullahy, J. (2003). Generalized Modelling Approaches to Risk Assessments of Skewed Outcomes Data. Technical Working paper 293, National Bureau of Economic Research, 1050 Massachusetts Avenue, Cambridge, M A 02138, October 2003, @ http://www.nber.org/papers/T0293
Nevitt, J. and Tam, H. P. (1998). A Comparison of Robust and Nonparametric Estimators Under the Simple Linear Regression Model, Multiple Linear Regression Viewpoints, Vol. 25, pp 54 – 69.
Pollock, D. S. G. 2014, Econometrics: A Historical Guide for the Uninitiated, Working Paper No. 14/05, February 2014, University of Leicester, UK.
The MIT Press, http://www.jstor.org/stable/1926296
Tiku, M. L., Tau, W. Y. and Balakrishnan N. (1986). Robust Inference, Marcel Dekker, New York.
Wooldridge, J. M. 2013, Introductory Econometrics: A Modern Approach. 5th ed. Mason, Ohio: South-Western Cengage Learning.
Zeckhauser, R. and Thompson, M. (1970). Linear Regression with Non-Normal Error Terms, The Review of Economics and Statistics, Vol. 52, No. 3 (Aug., 1970), pp. 280-286
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