Course syllabus - Methods of Statistical Inference

Objectives

Statistical analysis of real market data has an important role in analytical finance and economics. The course aims to equip students with the skills required for statistical inference. The course presents the main concepts and methods of statistical inference, such as estimation, confidence intervals, hypothesis testing, regression analysis and analysis of variances. It is anticipated that Matlab and other software will be used throughout the course.

Learning outcomes

At the end of the course the student is expected to be able to:

- describe and apply random sampling and statistical inference, in particular, the notions statistic, estimator, population, random sample, population distribution and sampling distribution
- describe point estimation, the main methods of estimation and the main properties of estimators, and apply them to data
- construct confidence intervals for unknown parameters
- describe and apply the main methods and concepts of hypotheses testing
- describe and apply the main methods and concepts of linear regression models
- describe and apply analysis of variance for a one-way layout
- describe and apply analysis of categorical data using Chi-square tests

Course content

Review of Probability: probability, random variables, distributions, expectations, sampling distributions, sampling from normal distribution, Estimation: unbiased estimates and mean square error, selection of sample size, efficiency, consistency, sufficiency, minimum variance estimation, moment estimation, maximum likelihood estimation. Confidence Intervals: two-sided and one-sided intervals, coverage probability, confidence intervals for parameters of normal distributions, pivots. Hypothesis Testing: error probabilities, likelihood ratio tests, tests for parameters of normal distribution, power of tests, Neyman-Pearson lemma, hypothesis testing and confidence intervals, p-values. Regression Analysis: linear models, estimation by least squares, inference for regression parameters, regression prediction. Analysis of Variance: one-way layout analysis, ANOVA tables, statistical inference for one-way layout.

Tuition

Lectures combined with exercises. Work with and presentation of written reports.

Specific requirements

At least totally 60 credits in the technical, natural sciences, business administration or economics areas including Probability 7.5 credits, of which 3 credits must be completed at the beginning of the course, or the equivalent, and a TOEFL test result, minimum score 173 (CBT), 500 (PBT) or 61 (iBT) or an IELTS test result with an overall band score of minimum 5,0 and no band score below 4,5. Exemption from the requirements of Swedish language proficiency will be made.

Examination

Seminar (SEM2), 1.5 credits, marks Pass (G
Written and/or oral examination (TEN3), 3 credits, marks Pass (G) or Pass with distinction (VG)
Written and/or oral examination (TEN4), 3 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass, Fail