Analysis of quantile regression as alternative to ordinary least squares

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    In this article, an alternative to ordinary least squares (OLS) regression based on analytical solution in the Statgraphics software is considered, and this alternative is no other than quantile regression (QR) model. We also present goodness of fit statistic as well as approximate distributions of the associated test statistics for the parameters. Furthermore, we suggest a goodness of fit statistic called the least absolute deviation (LAD) coefficient of determination. The procedure is well presented, illustrated and validated by a numerical example based on publicly available dataset on fuel consumption in miles per gallon in highway driving.


  • Keywords


    Quantile Regression; Model Validation; Stepwise Regression; Linear Programming.

  • References


      [1] Buhai, S., Quantile regressions: overview and selected applications. Unpublished manuscript. Tinbergan Institute and Erasmus University, (2004).

      [2] Cade, B. S. and Noon, B. R., “A gentle introduction to quantile regression for ecologists”, Frontiers in Ecology and the Environment, 1(8), (2003), pp: 412-420. http://dx.doi.org/10.1890/1540-9295(2003)001[0412:AGITQR]2.0.CO;23.

      [3] Chen, C., An introduction to Quantile Regression and the Quantreg Procedure. Sugi. (2004).

      [4] Cizek, P., Quantile Regression, in “XploRe Application Guide”, edited. by W. Härdle, Z. Hlavka, and S. Klinke, chap. 1, Springer, Berlin, pp: 19 – 48, (2003).

      [5] Green, H. M. and Kozek, A.S., Modeling weather data by approximate regression. Quantiles. Anziam. 44:C229-C248, (2003).

      [6] Koenker, R., Quantile Regression. New York, NY: Cambridge University Press, (2005). http://dx.doi.org/10.1017/CBO9780511754098.

      [7] Koenker, R. and G. Bassett, G. Jr., “Regression quantiles”, Econometrica, Vol. 1, (1978), pp: 33-50. http://dx.doi.org/10.2307/1913643.

      [8] Lee, “Quantile robust to outlier”. Statistics and numerical methods, (2005), pp: 35-57.

      [9] Wilby, R. L., Dawson, C. W., and Barrow, E. M., “SDSM - A decision support tool for the assessment of regional climate change impacts”. Environmental Modelling and Software, 17(2), (2002), pp: 147-159. http://dx.doi.org/10.1016/S1364-8152(01)00060-3.

      [10] Yu, K. and Moyeed, R. A., "Bayesian Quantile Regression", Statistics and Probability Letters, 54, (2001), pp: 437 - 447. http://dx.doi.org/10.1016/S0167-7152(01)00124-9.

      [11] Yu, K., Kerm, P.V. and Zhang, J., "Bayesian Quantile Regression: An Application to the wage Distribution in 1990s Britain". IRISS Working Paper 2004-10, CEPS/INSTEAD, Differdange, G. -D. Luxembourg. (2004).


 

View

Download

Article ID: 4686
 
DOI: 10.14419/ijasp.v3i2.4686




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.