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http://dx.doi.org/10.7465/jkdi.2013.24.1.33

Regression diagnostics for response transformations in a partial linear model  

Seo, Han Son (Department of Applied Statistics, Konkuk University)
Yoon, Min (Department of Statistics, Pukyong National University)
Publication Information
Journal of the Korean Data and Information Science Society / v.24, no.1, 2013 , pp. 33-39 More about this Journal
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;
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Times Cited By KSCI : 1  (Citation Analysis)
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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.   DOI   ScienceOn
4 Cook, R. D. (1993). Exploring partial residual plots. Technometrics, 35, 351-362.   DOI   ScienceOn
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.   DOI   ScienceOn
6 Gentleman, J. F. and Wilk, M. B. (1975). Detecting outliers. II. Supplementing the direct analysis of residuals. Biometrics, 31, 387-410.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
12 Larsen, W. A. and McCleary, S. J. (1972). The use of partial residual plots in regression analysis. Technometrics, 14, 781-790.   DOI   ScienceOn
13 Rousseeuw, P. J. and Driessen, K. V. (2006). Computing LTS regression for large data sets. Data Mining and Knowledge Discovery, 12, 29-45.   DOI   ScienceOn
14 Mallows, C. L. (1986). Augmented partial residual plots. Technometrics, 28, 313-320.   DOI   ScienceOn
15 Marasinghe, M. G. (1985). A multistage procedure for detecting several outliers in linear regression. Technometrics, 27, 395-399.   DOI   ScienceOn
16 Paul, S. R. and Fung, K. Y. (1991). A generalized extreme studentized residual multiple-outlier-detection procedure in linear regression. Technometrics, 33, 339-348.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
21 Weisberg, S. (2005). Applied linear regression, 3rd Ed., John Wiley, New York.