Browsing by Author "Thomas, Vernon John"

Now showing 1 - 2 of 2

The application of matrix theory to optimal design experiments : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy at Massey University
(Massey University, 1975) Thomas, Vernon John
A development of the theory of optimum experimental design is presented. The notation and proofs are in terms commonly used by statisticians, rather than in the earlier measure theory terms. The D-optimality equivalence theorem is extended to the singular case, and similar results derived for a number of other criteria. Atwood's theorem for special n-tic polynomials is extended to the case where not all parameters are of interest. Finally methods of constructing optimal designs are considered and extended to allow deletion of unsatisfactory points, and some numerical examples are included.
On some aspects of second order response surface methodology : a thesis presented in partial fulfilment of the requirements for the degree of M. Sc. in Mathematics at Massey University
(Massey University, 1972) Thomas, Vernon John
A unified development of the theoretical basis of response surface methodology, particularly as it applies to second order response surfaces, is presented. A rigorous justification of the various tests of hypothesis usually used is given, as well as a convenient means of making tests on whole factors, rather than on terms of a given degree, as is customary at present. Finally, the superimposition of some elementary classification designs on a response surface design is considered.