Testing of hypotheses with trinomials generated by guages
Testing of hypotheses with trinomials generated by guages
This thesis is concerned with the use of gauges in the testing of hypotheses. The first chapter includes a brief review of the use of gauges. The gauging generates trinomials and two statistics are considered; G, a general linear function of the trinomial frequencies and R a particularly simple form of G.The second chapter is concerned with the choice of parameters of G. A computationally simple procedure is suggested and it is shown that the procedure is nearly optimal in the sense of maximising power. Chapter 3 is concerned with general properties of R, including an investigation of the use of a normal approximation for R. The use of R for testing hypotheses about the mean of a normal variate is considered in some detail. The case of known variance is covered in Chapter 4 and Chapter 5 is concerned with the case of unknown variance. Chapter 6 is devoted to the use of R in sequential tests about the mean; one- and two-sided alternate hypotheses are considered. Use of gauges to test hypotheses about the means of two related variables is considered in Chapter 7. The case of bivariate normal variable with a known variance-covariance matrix is discussed in some detail. For the case of unknown variance-covariance matrix, an - approximation to the distribution of the test statistic, under the null-hypothesis, is suggested. Finally, some suggestions for further work are made in Chapter 8.
University of Southampton
1978
Hirji, Taj
(1978)
Testing of hypotheses with trinomials generated by guages.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
This thesis is concerned with the use of gauges in the testing of hypotheses. The first chapter includes a brief review of the use of gauges. The gauging generates trinomials and two statistics are considered; G, a general linear function of the trinomial frequencies and R a particularly simple form of G.The second chapter is concerned with the choice of parameters of G. A computationally simple procedure is suggested and it is shown that the procedure is nearly optimal in the sense of maximising power. Chapter 3 is concerned with general properties of R, including an investigation of the use of a normal approximation for R. The use of R for testing hypotheses about the mean of a normal variate is considered in some detail. The case of known variance is covered in Chapter 4 and Chapter 5 is concerned with the case of unknown variance. Chapter 6 is devoted to the use of R in sequential tests about the mean; one- and two-sided alternate hypotheses are considered. Use of gauges to test hypotheses about the means of two related variables is considered in Chapter 7. The case of bivariate normal variable with a known variance-covariance matrix is discussed in some detail. For the case of unknown variance-covariance matrix, an - approximation to the distribution of the test statistic, under the null-hypothesis, is suggested. Finally, some suggestions for further work are made in Chapter 8.
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Published date: 1978
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Local EPrints ID: 459850
URI: http://eprints.soton.ac.uk/id/eprint/459850
PURE UUID: e659a651-f22c-41d7-912a-c003a9f21633
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Date deposited: 04 Jul 2022 17:20
Last modified: 04 Jul 2022 17:20
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Author:
Taj Hirji
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