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TIME SERIES ANALYSIS

Stationary and non-stationary of series: removal of trend and seasonality by differencing. Moments and auto-correlation. Models: simple AR and MA models (mainly AR(1), MA(1)): moments and auto-correlations; the conditions of stationarity: invertibility. Mixed (ARMA) models, and the AR representation of MA and ARMA models. Yule-Walker equations and partial auto-correlations (showing forms for simple AR, MA models). Examples showing simulated series from such processes, and sample auto-correlations and partial auto-correlations.

Course Code: 
STA 406
No. of Credits: 
3
Level: 
Level 400
Course Semester: 
First Semester
Pre-requisite: 
STA 303
Select Programme(s): 
Statistics

INTRODUCTION TO STOCHASTIC PROCESSES

Preliminary concepts: the nature of a stochastic process, parameter space and state space. Markov processes and Markov chains. Renewal processes. Stationary processes. Markov chains: First order and higher order transition probabilities. Direct computation for two-state Markov chains. The Chapman-Kolmogorov equations. Unconditional state probabilities. Limiting distribution of a two-state chain. Classification of states. Closed sets and irreducible chains. Various criteria for classification of states. Queuing processes: characteristics and examples. Differential equations for a generalised queuing model. M/M/1 and M/M/S queues: characteristics of queue length, serving times and waiting time distributions. Inter-arrival times and traffic intensity. Applications to traffic flow and other congestion problems.

Course Code: 
STA 404
No. of Credits: 
3
Level: 
Level 400
Course Semester: 
First Semester
Pre-requisite: 
STA 301
Select Programme(s): 
Statistics

MULTIVARIATE METHODS

The course is specifically designed to introduce students to multivariate techniques.  It helps students to handle multivariate data effectively. Specific areas include: Structure of multivariate data. Inferences about multivariate means - Hotelling’s  ; likelihood ratio tests, etc.  Comparisons of several multivariate means - paired comparisons; one-way MANOVA; profile analysis.  Principal component analysis - graphing; summarizing sample variation, etc.  Factor analysis.  Discriminant analysis -  separation and classification for two populations; Fisher’s discriminant function; Fisher’s method for discriminating among several populations  Cluster analysis - hierarchical clustering; non-hierarchical clustering; multi-dimensional scaling.

Course Code: 
STA 405
No. of Credits: 
3
Level: 
Level 400
Course Semester: 
First Semester
Pre-requisite: 
STA 303
Select Programme(s): 
Statistics

STATISTICAL METHODS II

Further methods for discrete data: examples and formulation - binomial, multinomial and Poisson distributions.  Comparison of two binomials; McNeyman’s test for matched pairs; theory and transformations of variables; multiple linear regression; selection of variables ; use of dummy variables.    Introduction to logistic regression and generalized linear modeling.  Non-parametric methods.  Use of least squares principle; estimation of contrasts, two-way crossed classified data.  

Course Code: 
STA 403
No. of Credits: 
3
Level: 
Level 400
Course Semester: 
First Semester
Pre-requisite: 
STA 303
Select Programme(s): 
Statistics

STATISTICAL INFERENCE

Estimation theory - unbiased estimators; efficiency; consistency; sufficiency; robustness.  The method of moments.  The method of maximum likelihood.  Bayesian estimation - prior and posterior distributions; Bayes’ theorem; Bayesian significant testing and confidence intervals.  Applications - point and intervals.  Estimations of means, variances, differences between means, etc.  Hypothesis testing theory - test functions; the Neyman - Pearson Lemma; the power function of tests, Likelihood ratio test.  

Course Code: 
STA 413
No. of Credits: 
3
Level: 
Level 400
Course Semester: 
First Semester
Pre-requisite: 
STA 301
Select Programme(s): 
Statistics

DATA ANALYSIS II

Report writing and presentation ― organization, structure, contents and style of report.  Preparing reports for oral presentation.  Introduction to word processing packages, e.g.,  word for windows and latex.  Single- and two-sample problems; Poisson and binomial models.  Introduction to the use of generalized linear modeling in the analysis of binary data and contingency tables.  Simple and multiple linear regression methods; dummy variables; model diagnostics; one and two-way analysis of variance.  Data exploration method - summary and graphical displays.  Simple problems in forecasting. 

Course Code: 
STA 401
No. of Credits: 
3
Level: 
Level 400
Course Semester: 
First Semester
Pre-requisite: 
STA 304
Select Programme(s): 
Statistics

SAMPLING TECHNIQUES

This course will introduce students to the sampling methods.  The areas to cover include: Simple random sampling (with or without replacement)-estimation of sample size;

estimation of population parameters e.g., total and proportion; ratio estimators of population means, totals, etc.  Stratified random sampling - proportional and optimum allocations. 

Cluster sampling, systematic sampling, multistage sampling.

Course Code: 
STA 308
No. of Credits: 
3
Level: 
Level 300
Course Semester: 
Second Semester
Pre-requisite: 
STA 201 & STA 202/HND Statistics
Select Programme(s): 
Statistics

SAMPLING TECHNIQUES AND SURVEY METHODS

This course will introduce students to the sampling methods.  The areas to cover include: Simple random sampling (with or without replacement)-estimation of sample size; estimation of population parameters e.g., total and proportion; ratio estimators of population means, totals, etc.  Stratified random sampling - proportional and optimum allocations.  Cluster sampling, systematic sampling, multistage sampling.

Course Code: 
STA 302
No. of Credits: 
3
Level: 
Level 300
Course Semester: 
Second Semester
Pre-requisite: 
STA 201 & STA 202/HND Statistics
Select Programme(s): 
Statistics

DATA ANALYSIS I

Introduction to Statistical Software: Eg. SPSS, Minitab, R, Matlab. Statistical data – Data from designed experiments; sample surveys; observational studies.    Data exploration - sample descriptive techniques: measures of location and spread; correlation, etc.  Diagrammatic representation of data: the histogram; stem - and leaf -; box-plot; charts, etc.  Tabulation, interpretation of summary statistics and diagrams. Regression and Correlation Analysis: Simple Linear Regression. Interpretation of coefficients, Correlation and coefficient of determination. One-way ANOVA.

Course Code: 
STA 304
No. of Credits: 
3
Level: 
Level 300
Course Semester: 
Second Semester
Pre-requisite: 
STA 201, STA 202 or HND Statistics
Select Programme(s): 
Statistics

MULTIVARIATE DISTRIBUTIONS

Vector random variables: expected values of random vectors and matrices; covariance matrices; linear transforms of random vectors; further properties of the covariance matrix; singular and non-singular distributions; quadratic functions of random vectors. Distribution concepts: distribution of a random vector; multivariate moment generating functions. Transformation of random variables: vector transformation and Jacobian; change of variables in multiple integrals; distribution of functions of random vectors; some applications – the Beta-distribution family; the Chi-square, t – and  F – distributions. Order statistics: order transformation; joint distributions of order statistics; marginal distributions; alternative methods.  Multivariate normal distribution: definition and examples; singular and non-singular distributions; properties of the multivariate normal distribution; multivariate normal density; independence of multivariate normal vectors. Conditional distribution:

Course Code: 
STA 306
No. of Credits: 
3
Level: 
Level 300
Course Semester: 
Second Semester
Pre-requisite: 
STA 301
Select Programme(s): 
Statistics

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