Abstract
In this paper, the authors consider an adaptive recursive algorithm by selecting an adaptive sequence for computing M-estimators in multivariate linear regression models. Its asymptotic property is investigated. The recursive algorithm given by Miao and Wu (1996) is modified accordingly. Simulation studies of the algorithm is also provided. In addition, the Newton-Raphson iterative algorithm is considered for the purpose of comparison.
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References
Johnson R A and Wichern D W, Applied Multivariate Statistical Analysis, 2nd edition, Prentice-Hall, 1988.
Huber P J, Robust estimation of a location parameter, Annals of Mathematical Statistics, 1964, 35: 73–101.
Huber P J, Robust Statistics, Wiley, New York, 1981.
Martin R D and Masreliez C J, Robust estimation via stochastic approximation, IEEE Trans. Inform. Theory, 1975, 21: 263–271.
Maronna R A, Robust estimators of multivariate location and scatter, Annals of Statistics, 1976, 4: 51–67.
Chen X and Wu Y, Strong consistency of M-estimates in linear models, Journal of Multivariate Analysis, 1988, 27: 116–130.
Maronna R A, Martin D R, and Yohai V, Robust Statistics: Theory and Methods, Wiley, 2006.
Toma A, Optimal robust M-estimators using divergences, Statistics and Probability Letters, 2009, 1: 1–5.
Broniatowski M, Toma A, and Vajda I, Decomposable pseudodistances and applications in statistical estimation, Journal of Statistical Planning and Inference, 2012, 142: 2574–2585.
Bickel P J, One-step Huber estimates in the linear model, Journal of the Acoustical Society of America, 1975, 70: 428–434.
Englund J E, Holst U, and Ruppert D, Recursive M-estimators of location and scale for dependent sequences, Scandinavian Journal of Statistics, 1988, 15: 147–159.
Englund J E, Holst U, and Ruppert D, Recursive M-estimators for stationary, strong mixing processes — A representation theorem and asymptotic distributions, Stochastic Processes and Applications, 1989, 31: 203–222.
Englund J E, Multivariate recursive M-estimators of location for dependent sequences, Sequential Analysis, 1989, 8(3): 293–315.
Englund J E, Multivariate recursive M-estimate of location and scatter for dependent sequences, Journal of Multivariate Analysis, 1993, 45: 257–273.
Bai Z and Wu Y, Recursive algorithm for M-estimators of regression coefficients and scatter parameters in linear models, Sankhya Series B, 1993, 55(2): 199–218.
Miao B Q and Wu Y, Limiting behavior of recursive M-Estimators in multivariate linear regression models, Journal of multivariate analysis, 1996, 59: 60–80.
Wu Y, On consistency of recursive multivariate M-estimators in linear models, Robust Statistics, Data Analysis, and Computer Intensive Methods, 109 (Edited by Rieder H), 411–424, Springer-Verlag, New York, 1996.
Rubinstein R Y, Monte Carlo Optimization, Simulation, and Sensitivity of Queueing Networks, Wiley, 1986.
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This research is supported by the National Natural Science Foundation for Young Scientists of China under Grant No. 11101397 and the Natural Sciences and Engineering Research Council of Canada.
This paper was recommended for publication by Editor ZOU Guohua.
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Miao, B., Tong, Q., Wu, Y. et al. Selecting an adaptive sequence for computing recursive M-estimators in multivariate linear regression models. J Syst Sci Complex 26, 583–594 (2013). https://doi.org/10.1007/s11424-013-1113-x
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DOI: https://doi.org/10.1007/s11424-013-1113-x