Doctoral Degrees (Statistics and Actuarial Science)

Permanent URI for this collection

https://scholar.sun.ac.za/handle/10019.1/732

Browse

Browsing Doctoral Degrees (Statistics and Actuarial Science) by browse.metadata.advisor "Maritz, J. S."

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Edgeworth-corrected small-sample confidence intervals for ratio parameters in linear regression
    (Stellenbosch : Stellenbosch University, 2002-03) Binyavanga, Kamanzi-wa; Maritz, J. S.; Steel, S. J.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistical and Actuarial Science.
    ENGLISH ABSTRACT: In this thesis we construct a central confidence interval for a smooth scalar non-linear function of parameter vector f3 in a single general linear regression model Y = X f3 + c. We do this by first developing an Edgeworth expansion for the distribution function of a standardised point estimator. The confidence interval is then constructed in the manner discussed. Simulation studies reported at the end of the thesis show the interval to perform well in many small-sample situations. Central to the development of the Edgeworth expansion is our use of the index notation which, in statistics, has been popularised by McCullagh (1984, 1987). The contributions made in this thesis are of two kinds. We revisit the complex McCullagh Index Notation, modify and extend it in certain respects as well as repackage it in the manner that is more accessible to other researchers. On the new contributions, in addition to the introduction of a new small-sample confidence interval, we extend the theory of stochastic polynomials (SP) in three respects. A method, which we believe to be the simplest and most transparent to date, is proposed for deriving cumulants for these. Secondly, the theory of the cumulants of the SP is developed both in the context of Edgeworth expansion as well as in the regression setting. Thirdly, our new method enables us to propose a natural alternative to the method of Hall (1992a, 1992b) regarding skewness-reduction in Edgeworth expansions.