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Bounded influence nonlinear signed‐rank regression
Author(s) -
Bindele Huybrechts F.,
Abebe Asheber
Publication year - 2012
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.10134
Subject(s) - estimator , bounded function , mathematics , m estimator , outlier , rank (graph theory) , statistics , asymptotic distribution , least absolute deviations , robustness (evolution) , extremum estimator , nonlinear regression , monte carlo method , consistency (knowledge bases) , invariant estimator , regression analysis , efficient estimator , minimum variance unbiased estimator , discrete mathematics , combinatorics , mathematical analysis , biochemistry , chemistry , gene
In this paper we consider weighted generalized‐signed‐rank estimators of nonlinear regression coefficients. The generalization allows us to include popular estimators such as the least squares and least absolute deviations estimators but by itself does not give bounded influence estimators. Adding weights results in estimators with bounded influence function. We establish conditions needed for the consistency and asymptotic normality of the proposed estimator and discuss how weight functions can be chosen to achieve bounded influence function of the estimator. Real life examples and Monte Carlo simulation experiments demonstrate the robustness and efficiency of the proposed estimator. An example shows that the weighted signed‐rank estimator can be useful to detect outliers in nonlinear regression. The Canadian Journal of Statistics 40: 172–189; 2012 © 2012 Statistical Society of Canada