Equidistant regression modeling

Model Assisted Statistics and Applications

Volumn 2, Issue 2, 2007, Pages 71-80

  Lipovetsky, Stan ^a  

^a GfK Custom Research North America   (United States)

Author keywords

Absolute deviations; Efficient residual error variance; Least squares regression; Minimum distance difference; Nonlinear modeling

Indexed keywords

EID: 34547610449     PISSN: 15741699     EISSN: None     Source Type: Journal    
DOI: 10.3233/mas-2007-2202     Document Type: Article

References (30)

1. B. Abraham and J. Ledolter, Statistical Methods for Forecasting, Wiley, New York, 1983.
2. I.S. Abramson, On bandwidth variation in kernel estimates - a square-root law, Annals of Statistics 10 (1982), 1217-1223.
3. C.F. Ansley and P. Newbold, On the bias in estimates of forecast mean squared error, Journal of the American Statistical Association 76 (1981), 569-578.
4. G. Arminger, C.C. Clogg, and M.E. Sobel, eds, Handbook of Statistical Modeling for the Social and Behavioral Sciences, Plenum Press, New York, London, 1995.
5. S. Becker and Y. Le Cun, Improving the convergence of back-propagation learning with second order methods, in: Proceedings of the 1988 Connectionist Models Summer School, D.S. Touretzky, G.E. Hinton and T.J. Sejnowski, eds, Morgan Kaufmann, San Mateo, CA, 1988, pp. 29-37.
6. R. Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York, 1960.
7. E.A. Bender, Mathematical Methods in Artificial Intelligence, IEEE Computer Society Press, Los Alamitos, CA, 2000.
8. C.M. Bishop, Pattern Recognition and Machine Learning, Springer, New York, 2006.
9. R.A. Fisher, The Use of Multiple Measurements in Taxonomic Problems, Annals of Eugenics 7(part II) (1936), 179-188.
10. A. Giloni, B. Sengupta and J.S. Simonoff, A mathematical programming approach for improving the robustness of least sum of absolute deviations regression, Naval Research Logistics 53 (2006), 261-271.
11. J. Gurland and J. Sethuraman, How Pooling Failure Data May Reverse Increasing Failure Rates, Journal of the American Statistical Association 90 (1995), 1416-1423.
12. R.F. Gunst and R.L. Mason, Biased estimation in regression: An evaluation using mean squared error, Journal of the American Statistical Association 72 (1977), 616-628.
13. P. Hall and M.C. Minnotte, Higher order data sharpening for density estimation, Journal of the Royal Statistical Society 64(Ser. B) (2002), 141-157.
14. T.J. Hastie and R.J. Tibshirani, Generalized Additive Models, Chapman and Hall, London, New York, 1997.
15. M.G. Kendall and A. Stuart, The Advanced Theory of Statistics 2, New York, Hafner, 1973.
16. M. Levine, Bandwidth selection for a class of difference-based variance estimators in the nonparametric regression: A possible approach, Computational Statistics & Data Analysis 50 (2006), 3405-3431.
17. S. Lipovetsky and M. Conklin, Regression by Data Segments via Discriminant Analysis, Journal of Modern Applied Statistical Methods 4 (2005), 63-74.
18. S. Lipovetsky and M. Conklin, Data aggregation and Simpson's paradox gauged by index numbers, European Journal of Operational Research 172 (2006), 334-351.
19. S. Lipovetsky, Two-parameter ridge regression and its convergence to the eventual pairwise model, Mathematical and Computer Modelling 44 (2006), 304-318.
20. P. McCullagh and J.A. Nelder, Generalized Linear Models, Chapman & Hall, London, New York, 1997.
21. C.B. Read, Successive differences, in: Encyclopedia of Statistical Sciences 9, S. Kotz and N.L. Johnson, eds, Wiley, New York, 1988, pp. 65-68.
22. P.J. Rousseeuw, Least median of squared regression, Journal of the American Statistical Association 79 (1984), 871-880.
23. R.M. Royall and W.G. Cumberland, The finite-population linear regression estimator and estimators of its variance - an empirical study, Journal of the American Statistical Association 76 (1981), 924-930.
24. M. Schield, Simpson's Paradox and Cornfield's Conditions, in: ASA Proceedings of the Joint Statistical Meeting, Section on Statistical Education, Baltimore, MD, 1999, pp. 106-111.
25. B. Scholkopf and A.J. Smola, Learning with Kernels, MIT Press, Cambridge, MA, 2002.
26. B.W. Silverman, Using kernel density estimates to investigate multimodality, Journal of the Royal Statistical Society 43 Ser. B) (1981), 97-99.
27. B.W. Silverman, Density Estimation for Statistics and Data Analysis London, Chapman and Hall, 1986.
28. 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.
29. S-PLUS'2000, MathSoft Inc., Seattle, WA, 1999.
30. V.N. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995.