A comparison of various influential points diagnostic methods and robust regression approaches: Reanalysis of interstitial lung disease data

Applied Mathematical Sciences

Volumn 4, Issue 25-28, 2010, Pages 1367-1386

  Bagheri, Arezoo ^a   Midi, Habshah ^a   Ganjali, Mojtab ^b   Eftekhari, Samaneh ^b  

^a UNIVERSITY PUTRA MALAYSIA   (Malaysia)

^b SHAHID BEHESHTI UNIVERSITY   (Iran)

Author keywords

Likelihood displacement; Local influence; Robust regression methods

Indexed keywords

EID: 77953354577     PISSN: None     EISSN: 1312885X     Source Type: Journal    
DOI: None     Document Type: Article

References (44)

1. R. Andersen, Modern Methods for Robust Regression, Sara Miller McCune, SAGE publications, The United States of America, 2008.
2. R. D. Armstrong and M. T. Kung, Least absolute values estimates for a simple linear regression, problem, Applied Statistics, 27 (1978), 363-366.
3. A. Azzalini, A class of distribution which includes the normal ones, Scandinavian Journal of Statistics, 12 (1985), 171-178.
4. D. A. Belsley, E. Kuh and R. E. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, Wiley, New York,1980.
5. N. Billor, R. M. Loynes, Local Influence: A new approach, communications in statistics.-theory and methodology, 22 (1993), 1595-1611.
6. J. B. Birch, Some convergence properties of iterated reweighted least squares in the location model, Communications in Statistics - Simulation and Computers, B9 (1980), 359-369.
7. G. E. P. Box, Non-normality and tests on variances. Biometrika, 40 (1953), 318-335.
8. N. A. Campbell, H. P. Lopuhaä and P. J. Rousseeuw, On the calculation of a robust Sestimator of a covariance matrix, Statistics in Medicine, 17(23) (1998), 2685-2695.
9. H. C. Causton, J. Quackenbush and A. Brazma, Microarray Gene Expression Data Analysis: A Beginner's Guide, Blackwell publishing, 2003.
10. S. Chatterjee, A. S. Hadi, Influential observations, high leverage points, and outliers in linear regression, Statistical Science, 1 (3) (1986), 379-416.
11. C. W. Coakley, T. P. Hettmansperger, A bounded-influence, high-breakdown, efficient regression estimator, Journal of the American Statistical Association, 88 (1993), 872-880.
12. R. D. Cook, Assessment of local influence (with discussion), Journal of the Royal Statistical Society, Series. B: 48 (1986), 133-169.
13. R. D. Cook, Detection of influential observation in linear regression. Technometrics, 19 (1977), 15-18.
14. R. D. Cook, Influential observations in linear regression, Journal of American Statistical Association, 74 (1979), 169-174.
15. R. D. Cook, and D. M. Hawkins, Unmasking multivariate outliers and leverage points: comment, Journal of the American Statistical Association, 85 (1990), 640-44.
16. R. D. Cook, and Weisberg S., Residuals and Influence in Regression. London, Champan Hall, 1982.
17. N. R. Draper, and Smith H., Applied Regression Analysis, Wiley, New York, 1998.
18. A. S. Hadi, A new measure of overall potential influence in linear regression, Computational and Statistical Data Analysis, 14 (1992), 1-27.
19. F. R. Hampel, The influence curve and its role in robust estimation, Journal of the American Statistical Association, 69 (1974), 383-393.
20. E. Handschin, F. C. Schweppe, J. Kohlas, and A. Fiechter, Bad data analysis for power system state estimation, IEEE Transactions of Power Apparatus and Systems, PAS-94 (1975), 329-337.
21. R. W. Hill, Robust Regression When There Are Outliers in the Carriers, unpublished Ph.D, dissertation, Harvard University, Boston, MA, 1977.
22. P. J. Huber, Robust regression: asymptotic, conjectures, and Monte Carlo, The Annals of Statistics, 1 (1973), 799-821.
23. P. J. Huber, Robust statistics: A review. annual of mathematics and statistics, 43 (1972), 1041-1067.
24. P.J. Huber, Robust Statistics. John Wiley & Sons, New York, 2004.
25. P. J. Kempthorne, and M. B. Mendel, Unmasking multivariate outliers and leverage points: comment, Journal of the American Statistical Association, 85 (1990), 647-48.
26. D. C. Montgomery and E. A. Peck, Linear Regression Analysis, Wiley, New York, 1982.
27. F. Mosteller and J. W. Tukey, Data Analysis and Regression. Reading, MA: Addison-Wesley, 1977.
28. S. C. Narula, P. N. Saldiva, C. D. S. Andre, S. N. Elian, A. F. Ferreira, and V. Capelozzi, The minimum sum of absolute errors regression: a robust alternative to the least squares regression. Statistics in Medicine, 18 (1999), 1401-1417.
29. E. S. Pearson, The analysis of variance in cases of non-normal variation. Biometrika, 23 (1931), 114-133.
30. D. Pena, A new statistics for influence in linear regression. Technometrics, 47(1) (2005), 1-12.
31. W. Y. Poon, and Y. S. Poon, Total behavior of likelihood displacement. Statistica Sinica, 12 (2002), 599-607.
32. M. M. S. Rancel, and M. A. G. Sierra, A connection between local and deletion influence. Sankhya: The Indian Journal of Statistics, Series A, 62 (2000), 144-149.
33. P. J. Rousseeuw and C. Croux, Alternatives to the median absolute values, Journal of the American statistical association, 88 (1993), 1273-83.
34. P. J. Rousseeuw, and B. C. van Zomeren, Unmasking multivariate outliers and leverage points, Journal of the American Statistical Association, 85 (1990), 633-639.
35. P. J. Rousseeuw, and V. Yohai, Robust regression by means of S-estimators, Robust and Nonlinear Time series Analysis. Lecture Notes in Statistics, Springer Verlag, New York, 26 (1984), 256-272.
36. P. J. Rousseeuw, Least median of squares regression. Journal of the American Statistical Association, 79 (1984), 871-880.
37. P. J. Rousseeuw, Multivariate estimation with high breakdown point. Mathematical Statistics and Applications, Vol. B (1983), 283-297.
38. P. J. Rousseuw, and A. M. Leroy, Robust Regression and Outlier Detection, New York, John Willy, 2003.
39. D. Ruppert, and D. G. Simpson, Unmasking multivariate outliers and leverage points: comment, Journal of the American Statistical Association, 85 (1990), 644-646.
40. J. R. Simpson, New Methods and Comparative Evaluations for Robust and Biased-Robust Regression Estimation. PhD thesis, Arizona State University, 1995.
41. A. J. Stromberg, O. Hossjer, and D. M. Hawkins, The least trimmed differences regression estimator and alternatives, Journal of the American Statistical Association, 95 (2000), 853-864.
42. N. H. Timm, Applied Multivariate Analysis, Springer, 2002.
43. R. R. Wilcox, Introduction to Robust Estimation and Hypothesis Testing, 2th edition, Elsevier academic press, USA, 2005.
44. V.J. Yohai, High breakdown point and high efficiency robust estimates for regression. The Annals of Statistics, 15 (1987), 642-656.