Showing papers by "Joseph W. McKean published in 2013"

Weighted Wilcoxon Estimators in Nonlinear Regression

Abstract: Summary In this paper, we consider the estimation of parameters of a general near regression model. An estimator that minimises the weighted Wilcoxon dispersion function is considered and its asymptotic properties established under mild regularity conditions similar to those used in least squares and least absolute deviations estimation. As in linear models, the procedure provides estimators that are robust and highly efficient. The estimates depend on the choice of a weight function and diagnostics which differentiate between nonlinear fits are provided along with appropriate benchmarks. The behavior of these estimates is discussed on a real data set. A simulation study verifies the robustness, efficiency and validity of these estimates over several error distributions including the normal and a family of contaminated normal distributions.

Review of rank-based procedures for multicenter clinical trials.

Abstract: This article reviews nonparametric alternatives to the mixed model normal theory analysis for the analyses of multicenter clinical trials. Under a mixed model, the traditional analysis is based on maximum likelihood theory under normal errors. This analysis, though, is not robust to outliers. Robust, rank-based, Wilcoxon-type procedures are reviewed for a multicenter clinical trial for the mixed model but without the assumption of normality. These procedures retain the high efficiency of Wilcoxon methods for simple location problems and are based on a fitting criterion which is robust to outliers in response space. A simple weighting scheme can be employed so that the procedures are robust to outliers in factor (design) space as well as response space. These rank-based analyses offer a complete analysis, including estimation of fixed effects and their standard errors, and tests of linear hypotheses. Both rank-based estimates of contrasts and individual treatment effects are reviewed. We illustrate the ana...

On Multivariate Rank and Generalized Rank Regression

Abstract: Multivariate regression estimates based on ranks and generalized ranks are proposed. These estimates are based on a transformation and retransformation technique that uses Tyler's (1987) M-estimator of scatter. The proposed estimates are obtained by retransforming the componentwise rank-based estimate due to Davis and McKean (1993) and a componentwise generalized rank estimate. Asymptotic properties of the estimates are established under some regularity conditions. It is shown that both estimates have a multivariate normal limiting distribution. The influence function of the retransformed generalized rank estimate has a bounded influence in both factor and response spaces. It is shown thro ugh a simulation study that the transformed-retransformed R and GR estimates are highly efficient compared to the componentwis e R, GR and least absolute deviations estimates. Also, it is s hown that the new estimates perform better than the least squares estimate when the errors have a heavy tailed distribution. An example illustrating the estimation procedures is presented.