Statistical Methods for Scientists and Engineers. Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur. This course introduces some important topics in statistical methods used in science and engineering. Topics include: basic concepts of probability and distributions; parametric methods - point estimation, interval estimation, testing of hypotheses; multivariate analysis - multivariate normal distribution, Wishart and Hotelling's T-squared Distributions and their applications, classification of observations, principal component analysis; nonparametric methods - empirical distribution function, single sample problems, problems of location, Wilcoxon signed rank statistics, two sample problems, Mann-Whitney-Wilcoxon tests, scale problems, Kolmogorov-Smirnov two sample criterion, Hoeffding's U-statistics.
Lecture 11 - Point Estimation: Properties of Maximum Likelihood Estimation, Method of Scoring