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Course creator: Harmanpreet Singh Kapoor

##### Non Parametric Inference

Learning Outcomes: The students will be able to

●      Explain estimable parametric function.

●      Apply the concept of empirical distribution function.

●      Understand test for randomness.

●      Discuss about Rank Statistics and its limiting distribution.

Unit I                                                                       (15 Lecture Hours)

Estimable parametric functions, kernel, symmetric kernel, one sample U-Statistic. Two sample U-Statistic, asymptotic distribution of U-Statistics, UMVUE property of U-Statistics. Probability Inverse Transformation method and its application. Empirical distribution function, confidence intervals based on order statistics for quantiles, tolerance regions.

Unit II                                                                      (15 Lecture Hours)

Tests for randomness: Tests based on the total number of runs and runs up and down. Rank-order statistics. One sample and paired-sample techniques: sign test and signed-rank test. Goodness of fit problem: Chi-square and Kolmogorov-Smirnov tests. Independence in bivariate sample: Kendall’s and Spearman’s rank correlation.

Unit III                                                                     (15 Lecture Hours)

The General Two sample Problem: Wald Wolfwitz run test and Kolmogorov –Smirnov two sample test. Linear Rank Statistics: Linear Rank Statistics and its limiting distribution, Rank test, MP and LMP rank tests.

Unit IV                                                                     (15 Lecture Hours)

General two sample location and scale problem: Tests for two-sample location problem: Wilcoxon-Mann-Whitney, Terry-Hoeffding, Vander Waerden, Median tests. Tests for two-sample scale problem: Mood, Klotz, Capon, Ansari-Bradley, Siegel – Tukey and Sukhatme tests. Pitman asymptoitic relative efficiency. Tests for the c-sample problem: Kruskal-Wallis, Jonckheere- Terpstra tests. Concepts of Jackknifing, method of Quenouille for reducing bias, Bootstrap methods.

1.   A. C. Davison and D. V. Hinkley, Bootstrap Methods and their Applications, Cambridge University Press, 1997.

2.     J. D. Gibbons and S. Chakraborti, Nonparametrics Statistical Inference, 2nd Edition, Marcel Dekker, Inc, 2003.

3.     L. Wasserman, All of Nonparametric Statistics, 1st Edition, Springer, 2005.

4.     M. L. Puri and P. K. Sen, Nonparametric Methods in Multivariate Analysis, John Wiley and Sons, 1971.

5.     R. H. Randles and D. A. Wolfe, Introduction to the Theory of Nonparametric Statistics, Wiley, 1979.

6.      W. W. Daniel, Applied Nonparametric Statistics, 2nd Edition, Duxbury, 2000.    