Non-parametric Methods and Regression Analysis

Paper 1 : Non-parametric Methods and Regression Analysis

UNIT – I

Multivariate normal distributions, marginal and conditional distribution, Moment Generating

and Characteristics functions, Maximum likelihood estimation of mean vector and covariance
matrix, independence and joint sufficiency of these estimates. Distribution of linear
combination of components of multi normal variate.

UNIT – II

Order Statistics. Distributions of minimum, rth and maximum order statistic. Joint distribution
of rth and sth order statistics (in continuous case) Distribution of sample range & sample
median, for uniform and exponential distributions. Confidence interval of quantiles of order
p, tolerance and coverages.

UNIT – III

Non-parametric tests – Tests for randomness and test for goodness of fit. One sample tests :
sign test, Wilcoxon signed rank tests. Two sample tests : run test, Kolmogorov – Smirnov’s
test. Median test and Mann-Whitney U test. Mood tests and Sukhatme test for scale
parameter, Spearman’s rank correlation test, Kurskall-Wallis Test.

UNIT – IV

Linear regression model of full rank, Least squares theory. Estimation of parameters-OLSE
and MLE of β and test of hypotheses. R2 and adjusted R2. ANOVA table for regression,