Inferences Based on Robust Regression Estimators When There Is Multicolinearity
DOI:
https://doi.org/10.14738/assrj.55.4492Abstract
The paper deals with the goal of testing hypotheses about the slope parameters of a linear regression model when there is multicolinearity. A heteroscedastic method was recently derived based on a ridge estimator, but it does not guard against the deleterious impact of outliers. Several robust analogs of the ridge estimator have been proposed that might deal with this concern. The goal here is to find a robust method that performs reasonably well in simulations.
References
Adegoke, A. S., Adewuyi, E., Ayinde, K. & Lukman, A. F. (2016). A comparative study of some robust ridge and Liu estimators. Science World Journal, 11, No. 4. ISSN 1597-6343.
Arslan, O. & Billor, N. (2000). Robust Liu estimator for regression based on an M-estimator. Journal of Applied Statistic, 27, 39–47.
Bradley, J. V. (1978) Robustness? British Journal of Mathematical and} Statistical Psychology, 31, 144–152.
Clark, F., Jackson, J., Carlson, M., Chou, C.-P., Cherry, B. J., Jordan-Marsh M., Knight, B. G., Mandel, D., Blanchard, J., Granger, D. A., Wilcox, R. R., Lai, M. Y., White, B., Hay, J., Lam, C., Marterella, A. & Azen, S. P. (2011). Effectiveness of a lifestyle intervention in promoting the well-being of independently living older people: results of the Well Elderly 2 Randomise Controlled Trial. Journal of Epidemiology and Community Health, 66, 782–790. doi:10.1136/jech.2009.099754
Ertas, H., Kaçiranlar, S. & Güer (2017). Robust Liu-type estimator for regression based on M-estimator. Communications in Statistics–Simulation and Computation, 46, 3907–3932.
Hoaglin, D. C. (1985). Summarizing shape numerically: The g-and-h distribution. In D. Hoaglin, F. Mosteller & J. Tukey (Eds.) Exploring Data Tables Trends and Shapes. New York: Wiley, pp. 461--515.
Wilcox, R. (2018). Inferences Based on Robust Regression Estimators When There Is Multicolinearity. Advances in Social Sciences Research Journal,
Hoerl, A. E. & Kennard, R. W. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12, 55–67.
Kan, B., Alpu, Ö. & Yazici, B. (2013). Robust ridge and robust Liu estimator for regression based on the LTS estimator Journal of Applied Statistics, 40, 644–655
Kibria, B. M. G (2003). Performance of Some New Ridge Regression Estimators. Communication in Statistics-Simulation and Computation, 32, 419–435. DOI: 10.1081/SAC-120017499.
Liu, K. (1993). A new class of biased estimate in linear regression. Communications in Statistics–Theory and Methods, 22, 393–402.
Liu, K. (2003). Using Liu-type estimator to combat collinearity. Communications in Statistics–Theory and Methods, 32, 1009–1020.
Liu, R. G. & Singh, K. (1997). Notions of limiting P values based on data depth and bootstrap. Journal of the American Statistical Association, 92, 266–277.
Long, J. S. & Ervin, L. H. (2000). Using heteroscedasticity consistent standard errors in the linear regression model. American Statistician, 54, 217–224.
Lukman, A., Arowolo, O. & Ayinde, K. (2014). Some robust ridge regression for handling multicollinearity and outlier. International Journal of Sciences: Basic and Applied Research, 16, 192–202.
Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression} Analysis, 5th Ed.: New York: Wiley.
Rousseeuw, P. J. & Leroy, A. M. (1987). Robust Regression & Outlier Detection}. New York: Wiley.
Samkar, H. & Alpu, "{O}. (2010). Ridge regression based on some robust estimators. Journal of Modern Applied Statistical Methods, 9, Issue 2 , Article 17. DOI: 10.22237/jmasm/1288584960
Sen, P. K. (1968). Estimate of the regression coefficient based on Kendall’s tau. Journal of the American Statistical Association, 63, 1379–1389.
Theil, H. (1950). A rank-invariant method of linear and polynomial regression analysis. Indagationes Mathematicae, 12, 85–91.
Tukey, J. W. (1960). A survey of sampling from contaminated normal distributions. In I. Olkin, S. Ghurye, W.
Hoeffding, W. Madow & H. Mann (Eds.) Contributions to Probability and Statistics}. Stanford, CA: Stanford University Press (pp. 448-485). Wilcox, R. R. (2017). Introduction to Robust Estimation and Hypothesis Testing} 4th Ed. San Diego, CA: Academic Press
Wilcox, R. R. (2018). Multicolinearity and Ridge Regression: Results on Type I Errors, Power and Heteroscedasticity. Technical report, Dept. of Psychology, University of Southern California.
Yohai, V. J. (1987). High breakdown point and high efficiency robust estimates for regression. The Annals of Statistics, 15, 642–656.
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