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Statistics

Mathematical Statistics 3

Mathematical Statistics 3 consists of the five modules STAT301, STAT304, (STAT305 or STAT306), STAT307, STAT309 which must be passed separately.

Statistics 3

Statistics 3 consists of the six modules STAT302, STAT303, STAT304, STAT306, STAT307, and (STAT308 or STAT309) which must be passed separately.

Third Year Modules

STAT301: Statistical Inference (24 Credits)

This module consists of 66 single lectures and 28 tutorials during the first semester.

Pre-requisites: A previous pass in STAT201 and a pass or concurrent registration for either MAPM201 - 204 or MATH201 - 204.

Content:

Methods of finding estimators’. Criteria for evaluating estimators. Sufficiency and completeness. Confidence intervals: pivotal quantity method and general method. Theory of hypothesis testing: tests for Normal distribution, Binomial and Poisson tests, UMP tests, Generalized likelihood ratio test.

STAT302: Non-Parametric Statistical Procedures (10 Credits)

This module consists of 28 single lectures, 10 practicals and 10 tutorials during the first semester.

Pre-requisites: A previous pass in STAT203.

Content:

Inferential Single Sample Tests: Binomial Sign Ttest. Wilcoxon Signed-Rank Test. Kolmogorov-Smirnov Goodness of Fit. Randomness Tests. Inferential Two Independent Sample Tests: Mann-Whitney U Test. Kolmogorov-Smirnov Independence Test. Siegel Tukey and Moses Test of Variability. : Contingency tables, 2*2 and r*c. Median test. Wilcoxon Matched Pairs Signed Rank Tests. The McNemar Test. Inferential Tests For More Than Two Independent Samples: Bonferroni-Dunn, Newman-Keuls, Dunnet Tests. Kruskal-Wallis ANOVA. Inferential Tests For More Than Two Dependent Samples: Bonferroni-Dunn, Tukey’s HSD, Friedman ANOVA. Measures of Association: Spearman’s Rank-Order Correlation Coefficient, Goodman and Kruskal’s Gamma.

 

STAT303: Econometric Models (14 Credits)

This module consists of 38 single lectures, 14 practicals and 14 tutorials during the first semester.

Pre-requisites: A previous pass in STAT203.

Content:

Single-equation econometric models: Specification, estimation and testing. Distributed Lag Models. Koyck Lag Models. Multi-equation econometric models: Specification, Identification and Estimation: The Hausman test for simultaneity and OLS, 2SLS, 3SLS, FIML and SUR Estimation. Introduction to simulation models.

 

STAT304: Special Topics in Statistics (6 Credits)

This module consists of 18 single lectures and 12 tutorials during the first semester.

Pre-requisites: A previous pass in one of STAT201 or STAT202

Content:

Sample CDF and it’s use for estimation. Order statistics. Sample median, sample range. Tests for goodness of fit: Pearson’s test, Kolmogorov-Smirnov test. Bayesian statistical analysis. Prior and posterior distributions. Conjugate families of distributions. Loss function. Bayes estimators. Bayesian test procedures. Bayesian confidence intervals.

 

STAT305: Theory of Linear Models (10 Credits)

This module consists of 28 single lectures, 10 practicals and 10 tutorials during the second semester.

Pre-requisites: A previous pass in one of STAT201 or STAT202 and concurrent registration or a previous pass in both MATH203 - 204.

Content:

Generalised inverse matrix, elementary matrix, projection matrix, general linear model (LM), least square estimation, maximum likelihood estimation, estimable functions, Gauss-Markov theorem, Statistical methods based on LM: linear regression, polynomial regression, categorical data regression, one way Analysis of Variance (ANOVA), two-way ANOVA, paired comparisons model.

 

STAT306: Experimental Design and ANOVA (10 credits)

This module consists of 28 single lectures, 10 practicals and 10 tutorials during the second semester.

Pre-requisites: A previous pass in STAT203

Content:

Basic concepts: experimental unit, factors, levels and treatments. Designs: Completely randomized design. Randomized block design. Factorial designs. ANOVA of completely randomized, randomized block, and factorial experiments. The regression approach for analyzing data generated by experimental designs. Multiple comparisons of treatment means.

 

STAT307: Time Series Analysis (10 Credits)

This module consists of 28 single lectures, 10 practicals and 10 tutorials during the second semester.

Pre-requisites: A previous pass in STAT203.

Content:

Properties of stochastic time series models. Extrapolation and Smoothing. Forecasting: Moving averages, exponential smoothing and the Holt-Winters model, regression models and autoregressive error models. The Box-Jenkins approach: ARMA and ARIMA models.

 

STAT308: Advanced Probability Theory (10 Credits)

This module consists of 28 single lectures, 10 practicals and 10 tutorials during the second semester.

Pre-requisites: A previous pass in STAT201

Content:

Axiomatic theory of probability measure. Field of events, Sigma-algebra of events, probability space, statistical independence of probability spaces and events. Random variables (RV). Cumulative distribution function (CDF) and classification of the RV. Random vectors and their classification, Stieltjes integration. Functions of random variables, Moments, moment generating function and characteristic function. Special distributions: Chi-square, Student and Fisher distribution. Multivariate Normal Distribution.

 

STAT309: Operations Research (10 Credits)

This module consists of 28 single lectures, 10 practicals and 10 tutorials during the second semester.

Pre-requisites: A previous pass in one of STAT201 or STAT202

Content:

OR objectives and models. Linear programming, canonical and standard form. Structure of solution space, extreme points. Basic and non-basic variables, simplex algorithm and simplex table. Two-phase technique. Degeneracy. Transportation technique. Assignment problem, Hungarian method. Basics of Duality theory.