Probability review. Experimental and observational data. Descriptive statistics, graphical representation and exploratory data analysis. Sample distribution, precision calculation and sample size. Introduction to the bootstrap method, bootstrap hypothesis test. Statistical model, sufficient statistics and exponential family. Point estimation: method of moments and maximum likelihood. Estimator properties: distribution, consistency, vis, efficiency. Hypothesis Tests: Neyman-Pearson approach and statistical decision theory, likelihood ratio test, Wald test, types of error, power function, uniformly more powerful tests. Estimation of intervals: confidence interval, inversion method, pivot method, asymptotic approximation. ANOVA. Fundamentals of the linear regression model. Least squares method, hypotheses about the linear model.
Basic Information
Mandatory:
- Keener, R. W. (2011). Theoretical statistics: Topics for a core course. Springer.
Complementary:
- Bickel, P. J., Doksum, K. A. (2001). Mathematical statistics: basic ideas and selected topics. Vol I. Englewood Cliffs, NJ: Prentice Hall.
- Casella, G., & Berger, R. L. (2002). Statistical inference. Pacific Grove, CA: Duxbury.
- Schervish, M. J. (2012). Theory of statistics. Springer Science & Business Media.