Formulating robust regression estimation as an optimum allocation problem

Journal of Statistical Computation and Simulation

Volumn 72, Issue 9, 2002, Pages 687-705

  Camarinopoulos, L ^a   Zioutas, G ^b  

^a UNIVERSITY OF PIRAEUS   (Greece)

^b ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

Author keywords

Bounded influence; Efficiency; Leverage point; Monte Carlo simulation; Outlier; Quadratic programming; Robust regression

Indexed keywords

EID: 0036026580     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949650214267     Document Type: Article

References (26)

1. Armstrong, R. and Frome, E.L. (1976). A comparison of two algorithms for absolute deviation curve fitting. Journal of the American Statistical Association, 71, 328-330.
2. Arthanari, T.S. and Dodge, Y. (1993). Mathematical Programming in Statistics. John Wiley & Sons, Inc.
3. p- approximation. In: Rosen, J.B., Mangasarian, O.L. and Ritter, K. (Eds.), Nonlinear Programming. Academic Press, New York, pp. 447-464.
4. 1 linear approximation. SIAM J. Numer. Anal., 10, 839-848.
5. Coakley, C.W. and Hettmansperger, T.P. (1993). A bounded influence, high breakdown, efficient regression estimator. Journal of the American Statistical Association, 88, 872-880.
6. Giltinan, R.J., Caroll, R.J. and Ruppert, D. (1986). Some new estimation methods for weighted regression when there are possible outliers. Technometrics, 28, 219-230.
7. Hampel, F.R. (1978). Optimally bounding the gross error sensitivity and influence of position in factor space. Proceedings of the ASA Statistical Computing Section. ASA, Washington, DC, pp. 59-64.
8. Hampel, F.R., Ronchetti, E.M., Rousseuw, P.J. and Stahel, W.A. (1986). Robust Statistics, The Approach Based on Influence Functions. John Wiley, New York.
9. Handschin, E., Kohlas, J., Flechter, A. and Schweppe, F. (1975). Bad data analysis for power system estimation. IEEE Transactions on Power Apparatus and Systems, PAS-94(2), 329-337.
10. Hill, R.W. (1977). Robust regression when there are outliers in the carriers. Unpublished PhD Dissertation, Harvard University, Boston, MA.
11. Huber, P.J. (1973). Robust regression: Asymptotics, conjectures, and Monte Carlo. Annals of Statistics, 1, 799-821.
12. Huber, P.J. (1981). Robust Statistics. John Wiley, New York.
13. Huber, P.J. (1983). Minimax aspects of bounded-influence regression. Journal of the American Statistical Association, 78, 66-72.
14. Krasker, W.S. and Welsch, R.E. (1982). Efficient bounded-influence regression estimation. Journal of the American Statistical Association, 77, 595-604.
15. McKean, J.W., Sheather, S.J. and Hettmansperger, T.P. (1994). Robust and high-breakdown fits of polynomial models. Technometrics, 36(4), 409-415.
16. Mallows, C.L. (1973). Influence functions. Paper presented at the National Bureau of Economic Research Conference on Robust Regression in Cambridge, Massachusetts.
17. Mallows, C.L. (1975). On some topics in robustness. Unpublished Memorandum. Bell Telephone Laboratories, Murray Hill, New Jersey.
18. Mallows, C.L. (1983). Minimax aspects of bounded-influence regression [Discussion for the article of Huber (1983)]. Journal of the American Statistical Association, 78, 66-80.
19. Marazzi, A. (1993). Algorithms, Routines, and S Functions for Robust Statistics, Wadsworth and Brooks/Cole, Pacific Grove, California.
20. Pariente, S. and Welsch, R.E. (1977). Ridge and robust regression using parametric linear programming. Working Paper, MIT, Alfred P. Sloan School of Management.
21. Rousseeuw, P.J. and Leroy, A.M. (1987). Robust Regression and Outlier Detection. Wiley, New York.
22. Simpson, J.R. and Montogomery, D.C. (1996). A biased-robust regression technique for the combined outlier-multicollinearity problem, J. Statist. Comput. Simul., 56, 1-22.
23. Simpson, J.R. and Montogomery, D.C. (1998). A robust regression technique using compound estimation. Naval Research Logistics, 45(2), 125-139.
24. Snyder, R.D. (1982). Robust time series analysis. European Journal of Operational Research, 9, 168-174.
25. Welsch, R.E. (1980). In: Kmenta, J. and Ramsey, J.B. (Eds.), Regression Sensitivity Analysis and Bounded-Influence Estimation, Evaluation of Econometric Models. Academic Press, New York, pp. 153-167.
26. Zioutas, G., Camarinopoulos, L. and Bora Senta, E. (1997). Robust autoregressive estimates using quadratic programming. European Journal of Operational Research, 101, 486-498.