Bounded influence nonlinear signed‐rank regression

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     

Rank-Based Classification Using Robust Discriminant Functions

The Pareto distribution model assumption in the peaks over threshold method, will be tested by making using of the Kolmogorov–Smirnov goodness of fit method. Pareto distributed variables can be transformed to exponential, and the test will be for exponentiality. It was found that the statistic can be used as an indication of where to choose the threshold and to check the Pareto model assumption.