B029777 - STATICAL INFERENCE AND COMPUTATIONAL METHODS

Italian

Introduction to Statistical Inference. Principles of data reductions. Point estimation. Testing of Hypotheses. Interval estimation. An introduction to some advanced topics. Computational methods in R.

Casella, G. and Berger L. R. (2002). Statistical Inference. Second Edition. Duxbury Press.

The aim of this course is to introduce students to the theory and practice of statistical inference and to the related computational strategies and algorithms.
Moreover the course aims to develop students' expertise to analyze inferential problems selecting the appropriate inferential methods, to implement the analyses in R, and to properly interpreter and describe the results of the analyses.

Basic knowledge of algebra, maths and statistics

Lectures, sessions of exercises and labs

Additional teaching material will be provided during the course through the e-learning platform

The exam consists of a written test, a test with exercises that require the use of the R software and an oral exam, aimed to evaluate students' comprehension, acquisition and elaboration skills. The written test will include both applied exercises (that may require the use of a pocket calculator) and theoretical exercises. The test with R will focus on computational methods. Students must pass the written test to take the oral exam.

INTRODUCTION TO STATISTICAL INFERENCE. Statistical model. Parametric statistical model. Exponential families. Regular exponential families. Location and scale families. Experiment and statistical model. Sampling from infinite population. Random sample and observed sample. Statistical models for random samples. An introduction to the main inferential problems. Inferential approaches: an overview.

STATISTICS AND SAMPLING DISTRIBUTIONS. Statistics. Sampling distributions. Sum, mean and variance for random samples. Sufficient statistics. Ancillary statistics. Complete statistics. Basu's theorem.

POINT ESTIMATION. Estimators: minimax estimators, Method of moments estimators, maximum Likelihood estimators. Properties of estimators: Unbiasedness, efficiency. Fisher information. Cramér-Rao inequality. Rao-Blackwell's theorem. Lehmann-Scheffè theorem. Asymptotic theory: consistency, estimators with Normal asymptotic distributions, asymptotic efficiency. Properties of Likelihood estimators. Properties of method of moments estimators.

TESTING OF HYPOTHESES. Formulation of the hypothesis testing problem. The Neyman-Pearson Theorem. Likelihood ratio tests. Most powerful tests.
Unbiased test. Asymptotic tests. Important examples. P-value: definition and interpretation. Some thought on the concepts of p-value and statistical significance. Inference with nuisance parameters Introduction to multiple test.

INTERVAL ESTIMATION, Pivotal quantities and method of pivots. Method of test inversion. Methods of evaluating interval estimators. Approximate maximum likelihood intervals.

MISCELLANEA. The Delta method. Bootstrap. Introduction to numerical optimization methods.

COMPUTATIONAL METHODS:
User-defined functions in R; Introduction to programming with R Random Variable Generation; Monte Carlo Methods; Bootstrap in R.