28174 - Inference

Course Unit Page

Academic Year 2018/2019

Learning outcomes

By the end of the course the student should know the basic theory of likelihood based statistical inference. In particular the student should be able: - to derive the maximum likelihood estimators and their properties - to derive likelihood-based interval estimates - to test statistical hypotheses according to Neyman and Pearson’s approach - to build statistical tests using the GLR criterion.

Course contents

Introduction to the statistical inference.The Likelihood function. Sufficient statistics.

Estimation theory.

Moments and maximum likelihood estimation method. Point estimation: finite and asymptotic properties of estimators. Interval estimation: the pivotal quantity method and asymptotical confidence intervals.

Hypothesis testing.

Neyman-Pearson theory. Null hypothesis and alternative hypothesis; Type I and Type II errors; power of a test. Rejection Region. Simple hypothesis and composite hypothesis. Simple null and alternative hypothesis: Neyman-Pearson's lemma. Generalized Likelihood Ratio Test.

Readings/Bibliography

Larsen R.J. and Marx M.L. "An introduction to mathematical statistics and its applications", Prentice Hall, 2012.

Azzalini A. "Statistical infernece based on the likelihood", Chapman & Hall/CRC, 2002.

Trosset (2008). An Introduction to Statistical Inference and Its Applications with R, Chapman & Hall/CRC.

Teaching methods

Lectures and tutorials

Assessment methods

The exam consists of a mandatory written exam and an optional oral exam. The exam paper consists of questions concerning the theoretical parts of the course and exercises aiming at evaluating if the students are able to solve statistical inference problems. During the exam the use of textbooks, notes and computers tools are not allowed.

Teaching tools

Teacher's notes available at the web-site http://www2.stat.unibo.it/cagnone.

Office hours

See the website of Silvia Cagnone