Review of different transformation techniques, modes of convergence, law of large numbers, and central limit theorem; Sampling distributions based on normal distributions, multivariate normal distribution.
Point estimation: sufficiency, Neymann-Fisher factorization theorem, unbiased estimation, method of moments, maximum likelihood estimation, consistency and asymptotic normality of maximum likelihood estimator.
Interval estimation: confidence coefficient and confident level, pivotal method, asymptotic confidence interval, Bootstrap confidence interval.
Hypothesis testing: type-I and type-II errors, power function, size and level, test function and randomized test, most powerful test and Neyman-Pearson lemma, likelihood ratio test, p-value
Multiple linear regression: least squares estimation, estimation of variance, tests of significance, interval estimation, multicollinearity, residual analysis, PRESS statistic, detection and treatment of outliers, lack of fit.
Multivariate analysis: principle component analysis, factor analysis, canonical correlations, cluster analysis.
Weights in different examinations are as follows:
For each examination, linear scaling will be used (if needed).
Letter grade based on your performance in 5 exams (3 quizzes, MS, ES)
following a relative grading scheme