Non-Parametric Statistical Inference

Syllabus Details

• Unit I:(One Sample Problems) Dichotomous data: proportion test, estimation, Bayes estimators; one-sample location: paired replicates data, signed rank test, associated estimator and confidence interval, sign test, associated estimator and confidence interval, asymptotic procedure.
• Unit II:(Two Sample and Multi-sample Problems) Two sample problems: two-sample location problem: rank sum test, associated estimator and confidence interval, robust rank test; two-sample dispersion: rank test for dispersion with medians equal, asymptotic test for dispersion with unequal medians; test for either location or dispersion; test for general differences in two populations; two proportions: approximate tests and confidence intervals for difference, exact test for difference, inference for the odds ratio, inference for k strata of 2×2 tables. Multi-sample problems: one-way layout: tests for general, ordered and umbrella alternatives, test for treatments versus a control, two and one sided tests for multiple comparisons, contrast estimation, simultaneous confidence intervals; two-way layout: test in RCBD for general and ordered alternatives, two and one-sided tests for multiple comparison, test for BIBD for general alternatives, asymptotic test, test for general alternatives for data from arbitrary incomplete block design, other tests for general alternatives, ordered alternatives, multiple comparisons, contrast estimation.
• Unit III:(Independence and Regression) Independence: test for independence based on signs, associated estimator and asymptotic confidence intervals; test for independence based on ranks, test for independence against broad alternatives. Regression: one regression line: test for the slope, estimator of slope, confidence interval for slope, estimator for intercept, prediction; multiple regression lines: asymptotic test for parallelism, asymptotic rank-based tests; nonparametric regression analysis: non-rank-based approaches.
• Unit IV:(Density Estimation) Density functions and histograms, kernel density estimation.

Course Learning Objective

1. Solve inferential problems where the conditions for the traditional parametric tools to be applied are not fulfilled.
2. Apply non-parametric methods to one sample, two sample and multiple sample inferential problems.
3. Determine non-parametric estimates of regression coefficients and carry out inference.
4. Apply non-parametric density estimates.

Recommended Books

1. Hollander, Myles, Wolfe, Douglas A. and Chicken, Eric. Nonparametric Statistical Methods. 3rd ed. Wiley, 2014
2. Gibbons, Jean Dickinson and Chakraborti, Subhabrata. Nonparametric Statistical Inference. 3rd ed. Marcel Dekker, 1992