Module Code - Title:

MS4214 - STATISTICAL INFERENCE

Year Last Offered:

2025/6

Hours Per Week:

Lecture

2

Lab

0

Tutorial

1

Other

0

Private

7

Credits

6

Grading Type:

N

Prerequisite Modules:

MS4213

Rationale and Purpose of the Module:

This course introduces students to the formalities of statistical inference with special emphasis on problems of estimation, confidence intervals, and hypothesis testing.

Syllabus:

The notion of a probability model : examples, the need for estimation, confidence intervals and hypothesis tests. Inference for normal data : chi-squared, t, F, confidence intervals, hypothesis tests, two means, two variances. Central Limit Theorem : normal approximation to the binomial, application to inference for a single proportion and the difference between two proportions, the chi-squared test for independence. The likelihood function : the maximum likelihood estimate (MLE), iterative methods for calculating MLE. Repeated sampling properties : bias, variance, mean squared error, Cramer-Rao theorem, efficiency, the large sample behaviour of maximum likelihood estimates. Interval estimation : pivotal quantities, confidence intervals, approximate confidence intervals based on the MLE. Hypothesis testing : test statistic, Type 1 and Type 2 errors, power function, the likelihood ratio test.

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

* Calculate the likelihood function, the score function and the information function based on observed realisations from commonly used probability distributions and densities, and in such settings calculate the maximum likelihood estimates of the parameters of interest * Write basic programmes with the statistical software package R to compute numerical likelihood maximization based on NewtonÆs method, FisherÆs method of scoring, and quasi-Newton methods * Calculate the Cramer-Rao lower bound, and the efficiency of estimators * Apply large sample properties for maximum likelihood estimates * Calculate tests of hypothesis based on likelihood theory * Calculate interval estimates based on likelihood theory

Affective (Attitudes and Values)

None

Psychomotor (Physical Skills)

None

How the Module will be Taught and what will be the Learning Experiences of the Students:

Lectures, homework and tutorials

Research Findings Incorporated in to the Syllabus (If Relevant):

Prime Texts:

Hogg, R.V. and Craig, A.T. (1995) Introduction to Mathematical Statistics (5th Edition) , Prentice-Hall, USA.

Cox,D.R. and Hinkley, D.V. (1974) Theoretical Statistics , Chapman and Hall.

Rice, J.A. (1995) Mathematical Statistics and Data Analysis (2nd Edition) , Duxbury

Silvey, S.D. (1970) Statistical Inference , Chapman and Hall.

Other Relevant Texts:

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

Kevin.Burke@ul.ie