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 OJS  Vol.4 No.1 , February 2014
Identifying Unusual Observations in Ridge Regression Linear Model Using Box-Cox Power Transformation Technique
Abstract: The use of [1] Box-Cox power transformation in regression analysis is now common; in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved deletion of influential data cases. The pioneer work of [2] studied local influence on constant variance perturbation in the Box-Cox unbiased regression linear mode. Tsai and Wu [3] analyzed local influence method of [2] to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox unbiased regression linear model. Many authors noted that the influential observations on the biased estimators are different from the unbiased estimators. In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model. Two real macroeconomic data sets are used to illustrate the methodologies.
Cite this paper: A. Jahufer, "Identifying Unusual Observations in Ridge Regression Linear Model Using Box-Cox Power Transformation Technique," Open Journal of Statistics, Vol. 4 No. 1, 2014, pp. 19-26. doi: 10.4236/ojs.2014.41003.
References

[1]   G. E. P. Box and D. R. Cox, “An Analysis of Transformation (with Discussion),” Journal of the Royal Statistical Society, Series-B, Vol. 26, 1964, pp. 211-252.

[2]   A. J. Lawrance, “Regression Transformation Diagnostics Using Local Influence,” Journal of the American Statistical Association, Vol. 83, No. 404, 1988, pp. 1067-1072.
http://dx.doi.org/10.1080/01621459.1988.10478702

[3]   C. L. Tsai and X. Wu, “Transformation Model Diagnostics,” Technometrics, Vol. 34, No. 2, 1992, pp. 197-202.
http://dx.doi.org/10.1080/00401706.1992.10484908

[4]   A. C. Atkinson, “Plots, Transformations and Regression,” Oxford University Press, Oxford, 1985.

[5]   R. D. Cook and P. C. Wang, “Transformations and Influential cases in Regression,” Technometrics, Vol. 25, No. 4, 1983, pp. 337-343. http://dx.doi.org/10.1080/00401706.1983.10487896

[6]   D. V. Hinkley and S. Wang, “More about Transformations and Influential Cases in Regression,” Technometrics, Vol. 30, No. 4, 1988, pp. 435-440.
http://dx.doi.org/10.1080/00401706.1988.10488439

[7]   R. D. Cook, “Assessment of Local Influence,” Journal of Royal Statistical Association, Series-B, Vol. 48, 1986, pp. 133-169.

[8]   C. L. Tsai and X. Wu, “Diagnostics in Transformation and Weighted Regression,” Technometrics, Vol. 32, No. 3, 1990, pp. 315-322. http://dx.doi.org/10.1080/00401706.1990.10484684

[9]   D. A. Belsley, E. Kuh and R. E. Welsch, “Regression Diagnostics: Identifying Influential Data and Sources of Collinearity,” Wiley, New York, 1980. http://dx.doi.org/10.1002/0471725153

[10]   A. E. Hoerl and R. W. Kennard, “Ridge Regression: Biased Estimation for Non-Orthogonal Problems,” Technometrics, Vol. 12, No. 1, 1970, pp. 55-67. http://dx.doi.org/10.1080/00401706.1970.10488634

[11]   A. E. Hoerl and R. W. Kennard, “Ridge Regression: Application to Non-Orthogonal Problems,” Technometrics, Vol. 12, No. 1, 1970, pp. 69-82. http://dx.doi.org/10.1080/00401706.1970.10488635

[12]   H. Sun, “Macroeconomic Impact of Direct Foreign Investment in China 1979-1996,” Blackwell Publishers Ltd., 1988.

[13]   J. W. Longley, “An Appraisal of Least Squares Programs for Electronic Computer from the Point of View of the User,” Journal of American Statistical Association, Vol. 62, No. 319, 1967, pp. 819-841. http://dx.doi.org/10.1080/01621459.1967.10500896

[14]   E. Walker and J. B. Birch, “Influence Measures in Ridge Regression,” Technometrics, Vol. 30, No. 2, 1988, pp. 221-227.
http://dx.doi.org/10.1080/00401706.1988.10488370

[15]   R. D. Cook, “Detection of Influential Observations in Linear Regression,” Technometrics, Vol. 19, No. 1, 1977, pp. 15-18.
http://dx.doi.org/10.2307/1268249

[16]   L. Shi and X. Wang, “Local Influence in Ridge Regression,” Computational Statistics & Data Analysis, Vol. 31, No. 3, 1999, pp. 341-353. http://dx.doi.org/10.1016/S0167-9473(99)00019-5

[17]   A. Jahufer and J. Chen, “Assessing Global Influential Observations in Modified Ridge Regression,” Statistics and Probability Letters, Vol. 79, No. 4, 2009, pp. 513-518.
http://dx.doi.org/10.1016/j.spl.2008.09.019

[18]   A. Jahufer and J. Chen, “Identifying Local Influential Observations in Liu Estimator,” Journal of Metrika, Vol. 75, No. 3, 2012, pp. 425-438. http://dx.doi.org/10.1007/s00184-010-0334-4

[19]   A. Jahufer and J. Chen, “Measuring Local Influential Observations in Modified Ridge Regression,” Journal of Data Science, Vol. 9, No. 3, 2011, pp. 359-372.

[20]   A. Jahufer, “Detecting Global Influential Observations in Liu Regression Model,” Open Journal of Statistics, Vol. 3, No. 1, 2013, pp. 5-11. http://dx.doi.org/10.4236/ojs.2013.31002

[21]   A. Jahufer and J. Chen, “Identifying Local Influence in Modified Ridge Regression Using Cook’s Method,” Sri Lankan Journal of Applied Statistics, Vol. 9, 2008, pp. 93-108.

[22]   J. Chen and A. Jahufer, “Assessment of Anomalous Observations in Liu Estimator,” Journal of Management, Vol. 5, 2009, 41-49.

 
 
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