Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Partially linear support vector orthogonal quantile regression with measurement errors

  • Received : 2014.10.24
  • Accepted : 2014.11.21
  • Published : 2015.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

Quantile regression models with covariate measurement errors have received a great deal of attention in both the theoretical and the applied statistical literature. A lot of effort has been devoted to develop effective estimation methods for such quantile regression models. In this paper we propose the partially linear support vector orthogonal quantile regression model in the presence of covariate measurement errors. We also provide a generalized approximate cross-validation method for choosing the hyperparameters and the ratios of the error variances which affect the performance of the proposed model. The proposed model is evaluated through simulations.

Keywords

References

  1. Carroll, R. J., Ruppert, D., Stefanski, L. A. and Crainiceanu, C. M. (2006). Measurement error in nonlinear models: A modern perspective, Chapman & Hall/CRC, New York.
  2. Chen, X., Hong, H. and Nekipelov, D. (2011). Nonlinear models of measurement errors. Journal of Economic Literature, 49, 901-7. https://doi.org/10.1257/jel.49.4.901
  3. Chesher, A. (2001). Parameter approximations for quantile regressions with measurement error, Working Paper CWP02/01, University College London, Dept. of Economics.
  4. Cho, D. H., Shim, J. and Seok, K. H. (2010). Doubly penalized kernel method for heteroscedastic autore-gressive data. Journal of the Korean Data & Information Science Society, 21, 155-162.
  5. Fuller, W. A. (1987). Measurement error models, Wiley, New York.
  6. He, X. and Liang, H. (2000). Quantile regression estimates for a class of linear and partially linear errors-in-variables models. Statistica Sinica, 10, 129-140.
  7. Hwang, C. and Shim, J. (2012). Smoothing Kaplan-Meier estimate using monotone suppot vector regression. Journal of the Korean Data & Information Science Society, 23, 1045-1054. https://doi.org/10.7465/jkdi.2012.23.6.1045
  8. Ma, Y. and Yin, G. (2011). Censored quantile regression with covariate measurement errors. Statistica Sinica, 21, 949-971. https://doi.org/10.5705/ss.2011.041a
  9. Mercer, J. (1909). Function of positive and negative type and their connection with theory of integral equations. Philosophical Transactions of Royal Society A, 415-446. https://doi.org/10.1098/rsta.1909.0016
  10. Nychka, D., Gray, G., Haaland, P., Martin, D. and O'Connell, M. (1995). A nonparametric regression approach to syringe grading for quality improvement. Journal of the American Statistical Association, 90, 1171-1178. https://doi.org/10.1080/01621459.1995.10476623
  11. Schennach, S. M. (2008). Quantile regression with mismeasured covariates. Econometric Theory, 24, 1010-1043.
  12. Shim, J. and Hwang, C. (2013). Expected shortfall estimation using kernel machines. Journal of the Korean Data & Information Science Society, 24, 625-636. https://doi.org/10.7465/jkdi.2013.24.3.625
  13. Shim, J. and Hwang, C. (2014). Estimating small area proportions with kernel logistic regressions models. Journal of the Korean Data & Information Science Society, 25, 941-949. https://doi.org/10.7465/jkdi.2014.25.4.941
  14. Shim, J., Kim, Y., Lee, J. and Hwang, C. (2012). Estimating value at risk with semiparametric support vector quantile regression. Computational Statistics, 27, 685-700. https://doi.org/10.1007/s00180-011-0283-z
  15. Vapnik, V. N. (1995). The nature of statistical learning theory, Springer, New York.
  16. Wang, H. J., Stefanski, L. A. and Zhu, Z. (2012). Corrected-loss estimation for quantile regression with covariate measurement errors. Biometrika, 99, 405-21. https://doi.org/10.1093/biomet/ass005
  17. Wei, Y. and Carroll, R. J. (2009). Quantile regression with measurement error. Journal of the American Statistical Association, 104, 1129-1143. https://doi.org/10.1198/jasa.2009.tm08420
  18. Yuan, M. (2006). GACV for quantile smoothing splines. Computational Statistics and Data Analysis, 50, 813-829. https://doi.org/10.1016/j.csda.2004.10.008

Cited by

  1. Geographically weighted kernel logistic regression for small area proportion estimation vol.27, pp.2, 2016, https://doi.org/10.7465/jkdi.2016.27.2.531
  2. Multioutput LS-SVR based residual MCUSUM control chart for autocorrelated process vol.27, pp.2, 2016, https://doi.org/10.7465/jkdi.2016.27.2.523
  3. Deep LS-SVM for regression vol.27, pp.3, 2016, https://doi.org/10.7465/jkdi.2016.27.3.827
  4. 국제곡물가격에 대한 기후의 고차 선형 적률 인과관계 연구 vol.28, pp.1, 2017, https://doi.org/10.7465/jkdi.2017.28.1.67
  5. 원유가격에 대한 환율의 인과관계 : 비모수 분위수검정 접근 vol.28, pp.2, 2017, https://doi.org/10.7465/jkdi.2017.28.2.361
  6. 심층 다중 커널 최소제곱 서포트 벡터 회귀 기계 vol.29, pp.4, 2015, https://doi.org/10.7465/jkdi.2018.29.4.895