M-methods in generalized nonlinear models

Probability and Statistical Models with Applications

Volumn , Issue , 2000, Pages 359-375

  Sanhueza, Antonio I ^a   Sen, Pranab K ^b  

^a UNIVERSIDAD DE LA FRONTERA   (Chile)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

Asymptotic normality; Efficiency; Estimating equations; Generalized additive models; M estimators; M tests; Robustness; Uniform asymptotic linearity

Indexed keywords

EID: 77953731878     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (34)

1. Beal, S. L. and Sheiner, L. B. (1988). Heteroscedastic nonlinear regression. Technometrics 30, 327-338.
2. Bickel, P. J. (1973). On some analogues to linear combinations of order statistics in the linear model. Annals of Statistics 1, 597 616.
3. Bickel, P. J. (1975). One-step Huber estimates in the linear model. Journal of the American Statistical Association 70, 428 434.
4. Carroll, R. J. and Ruppert, D. (1982). Robust estimation in heteroscedastic linear models. Annals of Statistics 10, 429 441.
5. Butter, R. (1975). Robust regression: different approaches to numerical solutions and algorithms. Research report 6, Fachgruppe fuer statistik, ETH, Zurich.
6. Gallant, A. R. (1975). Seemingly unrelated nonlinear regressions. Journal of Econometrics 3, 35-50.
7. Gallant, A. R. (1987). Nonlinear Statistical Models. John Wiley & Sons, New York.
8. Genning, C., Chinchilli, V. M., and Carter, W. H. (1989). Response surface analysis with correlated data: A nonlinear model approach. Journal of the American Statistical Association 84, 805-809.
9. Giltinan, D. M. and Ruppert, D. (1989). Fitting heteroscedastic regression models to individual pharmacokinetic data using standard statistical software. Journal of Pharmacokinetics and Biopharma ceutics 17, 601-614.
10. Hampel, F. R., Roussccuw, P. J., Ronclietti, E. and Stabel, W. (1986). Robust Statistics The Approach Based on Influence Functions. John Wiley & Sons, New York.
11. Hartley, H. O. (1961). The modified Gauss-Newton method for the fitting of nonlinear regression functions by least squares. Technometrics 3, 269-280.
12. Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman and Hall, London.
13. Hill, R. W. and Holland, P. W. (1977). Two robust alternatives to least squares regression. Journal of the American Statistical Association 72, 828-833.
14. Holland, P. W. and Welsch, R. E. (1977). Robust regression using iteratively reweighted least squares. Communications in StatisticsA6, 813-827.
15. Huber, P. J. (1964). Robust, estimator of a location parameter. Annals of Mathematical Statistics 35, 73-101.
16. Huber, P. j. (1973). Robust regression: asymptotics, conjetures and Monte-Carlo. Annals of Statistics 1, 799 821.
17. Huber, P. J. (1981). Robust Statistics. John Wiley & Sons, New York.
18. Jaeckel, L. A. (1972). Estimating regression coefficients by minimizing the dispersion of the residuals. Annals of Mathematical Statistics 43, 1449-1458.
19. Jureckova, J. and Sen, P. K. (1996). Robust Statistical Procedures, Asymtotics and Interrelations. John Wiley & Sons, New York.
20. Klein, R. and Yohai, V. J. (1981). Asymptotic behavior of iterative M-estimators for the linear model. Communications in StatisticsA10, 2373-2388.
21. Maronna, R. A. (1976). Robust M-cstimators of multivariate location and scatter. Annals of Statistics 4, 163-169.
22. Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics 11, 431 441.
23. McCullagh, P. (1983). Quasilikelihood functions. Annals of Statistics 11, 59-60.
24. McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models Second Edition. Chapman and Hall, UK.
25. Nclcler, J. A. and Wedderburn, R. W. M. (1972). Generalized linear models. Journal of Ihe Royal Statistical Society, Series A135, 370-384.
26. Schrader, R. M. and Hettmansperger, T. P. (1980). Robust analysis of variance based upon a likelihood ratio criterion. Biometrika67, 93-101.
27. Sen, P. K. (1982). On M-tests in linear models. Biometrika 69, 245-248.
28. Sen, P. K. (1998). Generalized linear and additive models: Robustness perspectives. Brazilian Journal of Probability and Statistics12, 91-112.
29. Sen, P. K. and Singer, J. M. (1993). Large Sample Methods in Statistics: An Introduction with Applications. Chapman and Hall, New York.
30. Singer, J. M. and Sen, P. K. (1985). M-methods in multivariate linear models. Journal of Multivariate Analysis 17, 168-184.
31. van Houwelingen, J. C. (1988). Use and abuse of variance models in regression. Biometrics 43,1073-1081.
32. Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika61, 439-447.
33. Yohai, V. J. and Marorma, R. A. (1979). Asymptotic behaviour of M-estimators for the linear model. Annals of Statistics 7, 258-268.
34. Zeger, S. L., Liang, K. Y., and Albert, P. S. (1988). Models for longitudinal data: A general estimating equation approach. Biometrics 44, 1049-1060.