Insegnamento a.a. 2016-2017

Go to class group/s: 20 - 21

DES-ESS (8 credits - I sem. - OB  |  2 credits SECS-S/01  |  6 credits SECS-S/05)

Course Director:
IGOR PRUENSTER

Course Objectives

The course is designed to provide an in-depth knowledge of the main aspects of statistical inference (point estimation and hypothesis testing), both from a conceptual and a technical point of view. Optimality principles are discussed for the main procedures, based on the properties of sufficiency, completeness, and ancillarity of statistics and based on the likelihood principle. The implications of such concepts are analyzed both within the finite sample case and in the asymptotic setting. Principles and techniques discussed in the course are relevant to the development and analysis of statistical models in many areas (e.g., in the linear model and its generalizations).

Course Content Summary

• Properties and results for random variables.
• Sufficient, ancillary, and complete statistics.
• Point estimation: method of moments and method of maximum likelihood. Comparison among estimators and optimality results (Mean Squared Error, Uniform Minimum Variance Estimators, Fisher’s information, Loss function).
• Hypothesis testing: criteria and construction of optimal tests within the Neyman-Pearson framework (power of tests). Tests based on the likelihood ratio. The role of the p-value and of tests of significance.
• Asymptotic considerations: consistent and asymptotically efficient estimators. Likelihood-based asymptotic tests and confidence intervals.
• Introduction to Bayesian inference and comparison to the classical framework.

Detailed Description of Assessment Methods

A written general exam or two partial written exams (one in the middle and one at the end of the course).
There are no different assessment method/exam program between attending and non attending students.

Textbooks

• N. MUKHOPADHYAY, Probability and Statistical Inference, Dekker-CRC Press, 2000.

Further detailed information is provided during the course.

Exam textbooks & Online Articles (check availability at the Library)

Prerequisites

Standard families of distributions. Transformations of random variables and vectors. Results on sampling from the normal distribution. Concepts of convergence for sequences of random variables.
These topics are dealt within the preparatory course, which is held at the very beginning of September. Attendance is strongly recommended.

Last change 23/05/2016 11:22