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Programme: BScHons Mathematical Statistics

Faculty of Natural and Agricultural Sciences
Minimum duration of study: 1 year
Total credits: 135

Programme information

Renewal of registration

  1. Subject to exceptions approved by the Dean, on the recommendation of the head of department, and in the case of distance education where the Dean formulates the stipulations that will apply, a student may not sit for an examination for the honours degree more than twice in the same module.
  2. A student for an honours degree must complete his or her study, in the case of full-time students, within two years and, in the case of after-hours students, within three years of first registering for the degree and, in the case of distance education students, within the period stipulated by the Dean. Under special circumstances, the Dean, on the recommendation of the head of department, may give approval for a limited extension of this period.

In calculating marks, General Regulation G.12.2 applies.

Apart from the prescribed coursework, a research project is an integral part of the study.

Admission requirements

  •  A relevant bachelor's degree with Mathematical Statistics on the 300-level is required.
  •  For BScHons in Mathematical Statistics, an average mark of 65% or more

              (i) in Mathematical statistics on the 300-level or

              (ii) in an equivalent statistical module(s) at an accredited institution is required.

  •  In addition to passing of the core modules, WST 312 is also required as prerequisite for BScHons and BComHons in Mathematical Statistics.
  • Students from other accredited institutions must comply with the same requirements based on equivalent modules at their institutions. In addition, students from other accredited institutions must also pass an entrance evaluation.
  • Student numbers are limited to a maximum of 40, collectively over all honours programmes in the Department of Statistics. Selection is based on performance in the prior degree, conditional on ii and iii above.
  •  Historical performance during prior studies will also be considered in selecting students. Specific attention will be given to modules repeated and duration of study.
  • Any additional entrance requirements as specified by the head of department in consultation with the departmental postgraduate selection committee.
  • International qualifications have to be evaluated by SAQA.

Promotion to next study year

The progress of all honours candidates is monitored biannually by the postgraduate coordinator/head of department. A candidate’s study may be terminated if the progress is unsatisfactory or if the candidate is unable to finish his/her studies during the prescribed period.

Pass with distinction

The BScHons degree is awarded with distinction to a candidate who obtains a weighted average of at least 75% in all the prescribed modules and a minimum of 65% in any one module.

Minimum credits: 135

Minimum credits:  135

Core credits:          60

Elective credits:      75

Other programme-specific information:

Details of compilation of curriculum are available from the Head of the Department of Statistics as well as from the departmental postgraduate brochure.

A candidate must compile his/her curriculum in consultation with the head of department or his representative. It is also possible to include postgraduate modules from other departments. Refer to the Departmental website for further information.

All honours students in Statistics/Mathematical Statistics should enrol for STK 796 which is a compulsory but non-credit-bearing module. The satisfactory completion of this module is a prerequisite for embarking on the research component of the degree programme.

Core modules

LMO 710 Linear models 710 Credits: 15.00

Module content:

Projection matrices and sums of squares of linear sets. Estimation and the Gauss-Markov theorem. Generalised t- and F- tests.

MVA 710 Multivariate analysis 710 Credits: 15.00

Module content:

Matrix algebra. Some multivariate measures. Visualising multivariate data.  Multivariate distributions. Samples from multivariate normal populations. The Wishart distribution. Hotelling’s T ² statistic. Inferences about mean vectors.

STK 796 Research orientation 796 Credits: 0.00

Module content:

A compulsory bootcamp must be attended as part of this module – usually presented during the last week of January each year (details are made available by the department ). The bootcamp will cover the basics of research to prepare students for the research component of their degree. The bootcamp should be done in the same year as registration for STK 795/WST 795. Each year of registration for the honours degree will also require the attendance of three departmental seminars. Students should ensure that their attendance is recorded by the postgraduate co-ordinator present at the seminars. The department approves the seminars attended. In addition, students are required to present their STK 795/WST 795 research in the department during the year of registration for these modules.

WST 795 Research report: Mathematical statistics 795 Credits: 30.00

Module content:

Refer to the document: Criteria for the research management process and the assessment of the honours essays, available on the web: under the Department of Statistics: postgraduate study.

Elective modules

EKT 720 Introduction to statistical learning 720 Credits: 15.00

Module content:

The emphasis is on the theoretical understanding and practical application of advances in statistical modelling. The following topics are covered: Single equation models: Nonparametric regression. Bootstrap procedures within regression analysis, k-nearest neighbour classification. Modelling categorical dependent variables - Logit/Probit models. Multiple outputs. Linear regression of an indicator matrix. Ridge regression. Non-linear regression modelling.  Some new developments in regression and classification.
Simultaneous equation models: Specification, identification and estimation of simultaneous equation models.

LMO 720 Linear models 720 Credits: 15.00

Module content:

The singular normal distribution. Distributions of quadratic forms. The general linear model. Multiple comparisons. Analysis of covariance. Generalised linear models. Analysis of categorical data.

MVA 720 Multivariate analysis 720 Credits: 15.00

Module content:

The matrix normal distribution, correlation structures and inference of covariance matrices. Discriminant analysis. Principal component analysis. The biplot. Multidimensional scaling. Exploratory factor analysis. Confirmatory Factor analysis and structural equation models.

PNP 720 Parametric stochastic processes 720 Credits: 15.00

Module content:

Introduction to statistical measure theory. Queueing processes: M/M/1; M/M/S; M/G/1 queues and variants; limiting distribution of the queue length and waiting times. Queuing networks. Some stochastic inventory and storage processes.

SFT 720 Sampling techniques 720 Credits: 15.00

Module content:

Simple random sampling. Estimation of proportions and sample sizes. Stratified random sampling. Ratio and regression estimators. Systematic and cluster sampling. Complex survey methodology. Handling of nonresponse.

SPC 780 Statistical process control 780 Credits: 15.00

Module content:

Quality control and improvement. Shewhart, cumulative sum (CUSUM), exponentially weighted moving average (EWMA) and Q control charts. Univariate and multivariate control charts.  Determining process and measurement systems capability. Parametric and nonparametric (distribution-free) control charts. Constructing control charts using Microsoft Excel and/or SAS. Obtaining run-length characteristics via simulations, the integral equation approach, other approximate methods and the Markov-chain approach.

TRA 720 Analysis of time series 720 Credits: 15.00

Module content:

In this module certain basic topics relating to discrete, equally spaced stationary and non-stationary time series are introduced as well as the identification, estimation and testing of time series models and forecasting. Theoretical results are compared to corresponding results obtained from computer simulated time series.

VMT 710 Distribution-free methods 710 Credits: 15.00

Module content:

A selection of: Nonparametric stochastic processes. Power and asymptotic power of distribution-free procedures. Theory and simulation. Asymptotic relative efficiency. Linear rank tests: Definition, properties and applications. Equal in distribution technique. Counting and ranking statistics. Introduction to one and two sample U-statistics. Permutation and distribution-free rank-like statistics. Multi-sample distribution-free tests, rank correlation and regression. Some nonparametric bootstrap and smoothing methods.