### Department of Biostatistics Seminar/Workshop Series

# Rank-Based Procedures for Linear and Non-Linear Models

## Kim Crimin, PhD

### Research Associate Professor, Department of Biostatistics, Vanderbilt University School of Medicine

### Wednesday, September 22, 1:30-2:30pm, MRBIII Conference Room 1220

Rank-based procedures for linear models generalize the Wilcoxon rank tests for simple location models and they inherit the robustness and high efficiency properties of the Wilcoxon rank tests. Given a general linear model, these rank-based procedures form a complete analysis, including estimation, confidence intervals, and tests of general linear hypotheses. Rank-based estimates are obtained from minimizing a norm based on a score function. The two most popular score functions are the sign-score function and the Wilcoxon score function, though there are many others, including a high-breakdown score function. The geometry of rank-based estimates is similar to that of Least Squares in the sense that the estimates are obtained by minimizing a norm, the difference being the Euclidean norm is replaced by a pseudo-norm. Based on geometry, rank-based estimating procedure can be extended to non-linear models. In this talk, rank-based procedures for linear and non-linear models are reviewed using data collected from drug discovery experiments.