Methods of Statistical Inference

Statistical analysis of real market data has an important role in analytical finance and economics. The course aims to equip students with the skills required for statistical inference. The course presents the main concepts and methods of statistical inference, such as estimation, confidence intervals, hypothesis testing, regression analysis, analysis of variances. It is anticipated that Matlab and other software will be used throughout the course. Review of Probability: probability, random variables, distributions, expectations, sampling distributions, sampling from normal distribution, Estimation: unbiased estimates and mean square error, selection of sample size, efficiency, consistency, sufficiency, minimum variance estimation, moment estimation, maximum likelihood estimation. Confidence Intervals: two-sided and one-sided intervals, coverage probability, confidence intervals for parameters of normal distributions, pivots. Hypothesis Testing: error probabilities, likelihood ratio tests, tests for parameters of normal distribution, power of tests, Neyman-Pearson lemma, hypothesis testing and confidence intervals, p-values. Regression Analysis: linear models, estimation by least squares, inference for regression parameters, regression prediction. Analysis of Variance: one-way layout analysis, ANOVA tables, statistical inference for one-way layout.