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Regression diagnostics for response transformations in a partial linear model

부분선형모형에서 반응변수변환을 위한 회귀진단

  • Received : 2012.11.07
  • Accepted : 2012.12.07
  • Published : 2013.01.31

Abstract

In the transformation of response variable in partial linear models outliers can cause a bad effect on estimating the transformation parameter, just as in the linear models. To solve this problem the processes of estimating transformation parameter and detecting outliers are needed, but have difficulties to be performed due to the arbitrariness of the nonparametric function included in the partial linear model. In this study, through the estimation of nonparametric function and outlier detection methods such as a sequential test and a maximum trimmed likelihood estimation, processes for transforming response variable robust to outliers in partial linear models are suggested. The proposed methods are verified and compared their effectiveness by simulation study and examples.

Keywords

Box-Cox transformation;C-step;maximum trimmed likelihood estimation;robustness

References

  1. Atkinson, A. C. and Riani, M. (2000). Robust diagnostic regression analysis, Springer, New York.
  2. Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations (with discussion). Journal of the Royal Statistical Society B, 26, 211-246.
  3. Cheng, T. (2005). Robust regression diagnostics with data transformations. Computational Statistics & Data Analysis, 49, 875-891. https://doi.org/10.1016/j.csda.2004.06.010
  4. Cook, R. D. (1993). Exploring partial residual plots. Technometrics, 35, 351-362. https://doi.org/10.1080/00401706.1993.10485350
  5. Fung, W., Zhu, Z., Wei, B. and He, X. (2002). Influence diagnostics and outlier tests for semiparametric mixed models. Journal of the Royal Statistical Society B, 64, 565?579. https://doi.org/10.1111/1467-9868.00351
  6. Gentleman, J. F. and Wilk, M. B. (1975). Detecting outliers. II. Supplementing the direct analysis of residuals. Biometrics, 31, 387-410. https://doi.org/10.2307/2529428
  7. Hadi, A. S. and Luceno, A. (1997). Maximum trimmed likelihood estimators: A unified approach, examples, and algorithms. Computational Statistics & Data Analysis, 25, 251-272. https://doi.org/10.1016/S0167-9473(97)00011-X
  8. Hadi, A. S. and Simonoff, J. S. (1993). Procedures for the identification of multiple outliers in linear models. Journal of the American Statistical Association, 88, 1264-1272. https://doi.org/10.1080/01621459.1993.10476407
  9. Jajo, N. K. (2005). A Review of robust regression an diagnostic procedures in linear regression. Acta Mathematicae Applicatae Sinica, 21, 209-224.
  10. Kianifard, F. and Swallow, W. H. (1989). Using recursive residuals, calculated on adaptively-ordered ob-servations, to identify outliers in linear regression. Biometrics, 45, 571-585. https://doi.org/10.2307/2531498
  11. Kianifard, F. and Swallow, W. H. (1996). A review of the development and application of recursive residuals in linear models. Journal of the American Statistical Association, 91, 391-400. https://doi.org/10.1080/01621459.1996.10476700
  12. Larsen, W. A. and McCleary, S. J. (1972). The use of partial residual plots in regression analysis. Technometrics, 14, 781-790. https://doi.org/10.1080/00401706.1972.10488966
  13. Mallows, C. L. (1986). Augmented partial residual plots. Technometrics, 28, 313-320. https://doi.org/10.2307/1268980
  14. Marasinghe, M. G. (1985). A multistage procedure for detecting several outliers in linear regression. Technometrics, 27, 395-399. https://doi.org/10.1080/00401706.1985.10488078
  15. Paul, S. R. and Fung, K. Y. (1991). A generalized extreme studentized residual multiple-outlier-detection procedure in linear regression. Technometrics, 33, 339-348. https://doi.org/10.1080/00401706.1991.10484839
  16. Rousseeuw, P. J. and Driessen, K. V. (2006). Computing LTS regression for large data sets. Data Mining and Knowledge Discovery, 12, 29-45. https://doi.org/10.1007/s10618-005-0024-4
  17. Seo, H. S. and Yoon, M. (2009). A dynamic graphical method for transformations and curvature specifica¬tions in regression. The Korean Journal of Applied Statistics, 22, 189-195. https://doi.org/10.5351/KJAS.2009.22.1.189
  18. Seo, H. S. and Yoon, M. (2010). Outlier detection methods using augmented partial residual plots in a partially linear model. Journal of the Korean Data Analysis Society, 12, 1125-1133.
  19. Stromberg, A. J. (1993). Computation of high breakdown nonlinear regression parameters. Journal of the American Statistical Association 88, 237-244.
  20. Tsai, C. L. and Wu, X. (1990). Diagnostics in transformation and weighted regression. Technometrics, 32, 315-322. https://doi.org/10.1080/00401706.1990.10484684
  21. Weisberg, S. (2005). Applied linear regression, 3rd Ed., John Wiley, New York.

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Acknowledgement

Supported by : 건국대학교