|TITLE||Multivariate Analysis 1|
|LEVEL||03 - Years 2, 3, 4 in Modular Undergraduate Course|
|DEPARTMENT||Statistics and Operations Research|
|DESCRIPTION||- Sampling from a Multivariate Normal Distribution
- Wishart Distribution and its Properties
- Hotelling's T2 Distribution and its Properties
- Distribution of Sample Mean and Covariance Matrix
- Inference about Mean Vectors
- Confidence Regions and Simultaneous Comparisons
- Comparing Two Populations, Profile Analysis
- Hypothesis Testing
- Principal Components
- Factor Analysis
The main aim of this study-unit is that of familiarizing the students with the theoretical and practical framework underlying the analysis of any data set that involves more than one variable.
1. Knowledge & Understanding:
By the end of the study-unit the student will:
- Be able to understand the role that the multivariate normal distribution plays in estimation and hypothesis testing of mean vectors and variance covariance matrices in a multivariate setting;
- Be familiar with various techniques that may be used in multivariate hypothesis testing, with special consideration being given to the likelihood ratio test;
- Have developed a sound background in multivariate estimation theory;
- Have a better appreciation of the role which matrix algebra plays, particularly in analysing covariance structures.
By the end of the study-unit the student will be able to:
- Use their theoretical knowledge and various statistical packages to perform simulations and to analyse real multivariate data;
- Use the material learnt to understand the theoretical and practical importance of multivariate techniques which have not been covered in this study-unit.
Main Text/s and any supplementary readings:
- Mardia, K.V., Kent, J.T. and Bibby, J.M. (1995) Multivariate Analysis, Academic.
- Knight, K. (1999) Mathematical Statistics, Chapman & Hall.
- Srivastava, M.S. and Khatri, C.G. (1979) An Introduction to Multivariate Statistics, North Holland.
- Johnson, R.A. and Wichern, D.W. (1992) Applied Multivariate Statistical Analysis, Prentice Hall Inc.
- Flury, B. (1997) A First Course in Multivariate Statistics, Springer.
- Hair J., Anderson R., Tatham R. and Black W., (1998) Multivariate Data Analysis, Prentice Hall I.
|ADDITIONAL NOTES||Pre-requisite Study-units: SOR1110, SOR2210 & SOR2220|
|STUDY-UNIT TYPE||Lecture and Practical|
|METHOD OF ASSESSMENT||
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Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2020/1. It may be subject to change in subsequent years.