Review of Probability and Distributions. Parametric Methods: Point estimation - methods of obtaining estimators. Interval estimation - confidence intervals for means, variances and proportions. Testing of Hypotheses - tests for parameters of normal populations and for proportions, Goodness of fit test and its applications. Multivariate normal, Wishart and Hotelling's T^{2} distributions and their applications, classification of observations, principal component analysis, canonical correlations and canonical variables. Nonparametric Methods - Empirical distribution function, single sample problems, problems of location, prediction intervals, Kolmogorov-Smirnov one sample statistics, sign test, Wilcoxon signed rank statistics, two sample problems, Mann-Whitney-Wilcoxon tests, scale problems, Kolmogorov-Smirnov two sample criterion, Hoeffding's U-statistics.

Module

Learning Units

Lectures

Module I

Review of Probability and Distributions: Rules for probability, random variables and their distributions, moments, special discrete and continuous distributions, laws of large numbers and central limit theorem, sampling distributions.

8

Module II

Parametric Methods: Point estimation – unbiasedness, consistency, UMVUE, sufficiency and completeness, method of moments, maximum likelihood estimation and method of scoring. Bayes, minimax and admissible estimators. Interval estimation - confidence intervals for means, variances and proportions. Testing of Hypotheses - tests for parameters of normal populations and for proportions, goodness of fit test and its applications.

7

Module III

Multivariate Analysis: Multivariate normal, Wishart and Hotelling's T^{2} distributions and their applications in testing of hypotheses problems. Classification of observations, principal component analysis, canonical correlations and canonical variables.

12

Module IV

Nonparametric Methods: Empirical distribution function, asymptotic distributions of order statistics, single sample problems, problems of location, prediction intervals, Kolmogorov-Smirnov one sample statistics, sign test, Wilcoxon signed rank statistics, two sample problems, Mann-Whitney-Wilcoxon tests, scale problems, Kolmogorov-Smirnov two sample criterion, Hoeffding's U-statistics.

13

Probability and distributions, Statistical Inference

An Introduction to Probability and Statistics by V.K. Rohatgi & A.K. Md. E. Saleh.

Modern Mathematical Statistics by E.J. Dudewicz & S.N. Mishra

Introduction to Probability and Statistics for Engineers and Scientists by S.M. Ross

An Introduction to Multivariate Analysis by T. W. Anderson

Nonparametric Statistical Inference by J.D. Gibbons & S. Chakraborti

Applied Multivariate Statistical Analysis by R.A. Johnson & D.W. Wichern

Nonparametric Inference by Z. Govindarajulu

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