About Statistical Inference
Definition, basic concepts and properties of a point estimator; Sufficiency, Completeness, exponential family of distributions; Parametric point estimation, methods of finding point estimates: unbiased estimation, method of moments, maximum likelihood and Bayesian; Parametric interval estimation, Confidence interval, Method of finding interval estimates: pivotal quantity method and large sample asymptotic distributions, some applications; Tests of hypotheses: basic concepts, Most powerful test, Neyman-Pearson lemma, Generalized likelihood ratio test, uniformly most powerful test, monotone likelihood ratio, unbiased test, applications: tests on the mean, the variance, several means, several variances; chi-square tests; relationship between tests and confidence intervals; Sequential test: sequential probability ratio test and some of its properties; Introduction to non-parametric methods: inference concerning the empirical distribution, quantiles and equality of two distributions