Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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M-quantile regression using kernel machine technique

  • Received : 2010.07.13
  • Accepted : 2010.09.06
  • Published : 2010.09.30
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Abstract

Quantile regression investigates the quantiles of the conditional distribution of a response variable given a set of covariates. M-quantile regression extends this idea by a "quantile-like" generalization of regression based on influence functions. In this paper we propose a new method of estimating M-quantile regression functions, which uses kernel machine technique. Simulation studies are presented that show the finite sample properties of the proposed M-quantile regression.

Keywords

References

  1. Abdous, B. and Remillard, B. (1995). Relating quantiles and expectiles under weighted-symmetry. Annals of the Institute of Statistical Mathematics, 47, 371-384. https://doi.org/10.1007/BF00773468
  2. Breckling, J. and Chambers, R. (1988). M-quantiles. Biometrika, 75, 761-771. https://doi.org/10.1093/biomet/75.4.761
  3. Chambers, R. and Tzavidis, N. (2006). M-quantile models for small area estimation. Biometrika, 93, 255-268. https://doi.org/10.1093/biomet/93.2.255
  4. Efron, B. (1991). Regression percentiles using asymmetric squared error loss. Statistica Sinica, 1, 93-125.
  5. Huber, P. J. (1981). Robust Statistics, Wiley, New York.
  6. Hwang, C. (2007). Kernel machine for Poisson regression. Journal of Korean Data & Information Science Society, 18, 767-772 .
  7. Hwang, C. (2008). Mixed effects kernel binomial regression. Journal of Korean Data & Information Science Society, 19, 1327-1334 .
  8. Hwang, C. (2010). Support vector quantile regression for longitudinal data. Journal of Korean Data & Information Science Society, 21, 309-316.
  9. Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica, 46, 33-50. https://doi.org/10.2307/1913643
  10. Kokic, P., Chambers, R., Breckling, J. and Beare, S. (1997). A measure of production performance. Journal of Business and Economic Statistics, 10, 419-435.
  11. Newey, N. K. and Powell, J. L. (1987). Asymmetric least squares estimates and testing. Econometrica, 55, 819-847. https://doi.org/10.2307/1911031
  12. Pratesi, M., Ranalli, M. G. and Salvati, N. (2009). Nonparametric M-quantile regression using penalized splines. Journal of Nonparametric Statistics, 21, 287-304. https://doi.org/10.1080/10485250802638290
  13. Schnabel, S. K. and Eilers, P. H. C. (2009). Optimal expectile smoothing. Computational Statistics and Data Analysis, 53, 4168-4177. https://doi.org/10.1016/j.csda.2009.05.002
  14. Seok, K., Hwang, C. and Cho, D. (2002). Prediction intervals for support vector machine regression. Communications in Statistics-Theory and Methods, 31, 1887-1898. https://doi.org/10.1081/STA-120014918
  15. Shim, J. and Lee, J. (2009). Kernel method for autoregressive data. Journal of Korean Data & Information Science Society, 20, 949-954.
  16. Shim, J. and Hwang, C. (2010). Support vector quantile regression with weighted quadratic loss function. Communications of the Korean Statistical Society, 17, 183-191. https://doi.org/10.5351/CKSS.2010.17.2.183
  17. Stone, C. J. (2005). Nonparametric M-regression with free knot splines. Journal of Statistical Planning and Inference, 130, 183-206. https://doi.org/10.1016/j.jspi.2003.05.002
  18. Takeuchi, I., Le, Q. V., Sears, T. D. and Smola, A. J. (2006). Nonparametric quantile estimation. Journal of Machine Learning Research, 7, 1231-1264.
  19. Taylor, J. W. (2008). Estimating value at risk and expected shortfall using expectiles. Journal of Financial Econometrics, 6, 231-252.
  20. Tzavidis, N., Salvati, N., Pratesi, M. and Chambers, R. (2008). M-quantile models with application to poverty mapping. Statistical Methods and Applications, 17, 393-411. https://doi.org/10.1007/s10260-007-0070-8
  21. Vinciotti, V. and Yu, K. (2009). M-quantile regression analysis of temporal gene expression data. Statistical Applications in Genetics and Molecular Biology, 8, Article 41.