MAT2790

Robust and nonparametric methods

Coordinators: Associate Professor P R Rayment and Mr J Hille

4 points - Second semester - Two hours of lectures and one 1-hour tutorial/ computing workshop per week - Gippsland and distance (odd-numbered years only) - Prerequisites: MAT1060 - Prohibitions: MAT3790, MAS3322 (to 1997)

Objectives On completion of this subject students will be able to apply appropriate robust and nonparametric procedures to a range of problems including location comparisons, matching samples to distributions and correlation measures where traditional parametric methods are inappropriate; utilise robust estimators of location and dispersion including trimmed and Winsorised estimates of location and estimates of linear regression coefficients.

Synopsis Comparison of roles of parametric and nonparametric inference procedures; assumptions and data types relevant to each; discussion of efficiency measures. Location tests for single samples; sign test and confidence interval for median; inference about median based on ranks - Wilcoxon signed rank test; transformation of ranks; large sample approximation. Matching samples to distributions; Kolmogorov tests; testing for normality. Paired sample procedures using signs and ranking methods; large sample approximations. Two independent samples; median test and the Wilcoxon-Mann-Whitney test; confidence intervals for median difference; large sample approximation. Three or more independent samples; the Kruskal-Wallis test; multiple comparison tests for location differences. Correlation procedures based on ranks; Spearman's rho and Kendall's tau; significance tests for each. Robustness; robust estimators including trimmed and Winsorised estimates of location; nonparametric regression including smoothing; robust estimation of simple linear regression. Introduction to resampling procedures including the jackknife and bootstrap.

Assessment Assignments (three): 10% each - Examination (two hours): 70%

Prescribed texts

Sprent P Applied nonparametric statistical methods 2nd edn, Chapman and Hall, 1993

Back to the 1999 Science Handbook