Best Critical Regions.
Introduction to Statistics. Random Variable, Mean, Variance, Standard Deviation and Mathematical Expectation. Discrete Distributions: Bernoulli trials and Bernoulli distribution, geometric distribution, Poisson distribution. Continuous Distributions: random variables of the continuous type, uniform distribution, exponential distribution, gamma distribution, chi-square distribution, normal distribution, t-distributions. Estimation: biased and unbiased esimators, convidence intervals for means, convidence intervals for variances, sample size, maximum error of the point estimate, Likelihood function, Maximum Likelihood Estimation (MLE), Asymptotic Distributions of Maximum Likelihood Estimators, Chebyshev's Inequality. Hypothesis: tests of statistical hypotheses, Type I error, Type II error, tests about proportions, null hypothesis, alternative hypothesis, significance level of the test, probability value, tail-end probability, standard error of the mean, tests about one mean and one variance, test of the equality of two independent normal distributions, best critical region, Neyman-Pearson Lemma, most powerful test, uniformly most powerful critical region, Likelihood Ratio tests, critical region for the likelihood ratio test. Pseudo-Numbers: uniform pseudo-random variable generation, congruential generators, shift-register generators, Fibonacci generators, Combinations of Generators (Shuffling). The Inverse Probability Method for Generating Random Variables. The Logistic Distribution.
Decision theory, estimation, confidence intervals, hypothesis testing. Introduces large sample theory. Asymptotic efficiency of estimates. Exponential families. Sequential analysis.
The course introduces statistical theory to prepare students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, building functional forms, regression algebra, Gauss-Markov optimality, finite-sample inference, consistency, asymptotic normality, heteroscedasticity, and autocorrelation.
