数理统计

This course is on the basis of “Probability Theory”. It will study the concepts and methods of statistics. The course will lay emphasis on the estimation and hypothesis testing, the two major areas of statistical inference. Through the study of this course, students will be equipped with both quantitative skills and qualitative perceptions essential for making rigorous statistical analysis of data. The course covers: distribution and density of function of random variables, order statistics, central limit theorem; Maximum likelihood estimator (MLE), moment estimator, Bayesian estimator, properties of estimators, limiting properties of MLE; Confidence interval estimations for normal mean, the difference of two normal means, normal variance, the ratio of two normal variances, and large-sample confidence intervals; Power function, Neyman-Pearson Lemma, likelihood ratio test, and goodness of fit test; Linear regression, least squares estimator, normal regression analysis, normal correlation analysis, and multiple linear regression; The sign test, the Wilcoxon signed-rank test, the rank-sum test.