| Summary: | Thesis (Ph.D.)--Memorial University of Newfoundland, 2001. Mathematics and Statistics Bibliography: leaves 170-178 Statistical inference under order restrictions is an important field in statistical science and has been studied and practiced widely. The utilization of the assumption of monotonicity increases the efficiency of statistical inference procedures. This can be found in the literature such as Ayer, Brunk, Ewing, Reid and Silverman (1955), Robertson and Wright (1974), Barlow and Ub- haya (1971), Lee (1981), Kelly (1989), Korn (1982), Schoenfeld (1986), Hayter (1990) and Lee (1996). In Chapter 2, we review some fundamental theories about the order restricted statistical inference including isotonic regression and test of a simply ordered hypothesis. -- In Chapter 3, we study a max-min interval procedure, a modification of Tukey's studentized range technique, to construct simultaneous confidence intervals for pairwise comparisons of response means by utilizing the prior knowledge of the monotonicity of the means. The improvement of the proposed max-min interval procedure is substantial. -- The one-sided simultaneous confidence lower bound is studied in Chapter 4. We investigate the incomplete optimization problem of maximizing simultaneous lower bounds for nonnegative contrasts considered by Marcus (1978). Significant improvements over Marcus' (1978) results, including a necessary and sufficient condition for the optimal solution and an efficient computation algorithm to compute the optimal lower bounds, are made. -- In Chapter 5, we introduce a one-sided multiple comparison test (OMCT) for testing the homogeneity of the means against the simple order alternative. It gives sharper one-sided simultaneous confidence lower bounds. This OMCT approach compares favorably with Hayter's (1990) and Marcus' (1978) approaches and it may be comparable to the least significant difference approach. -- The simultaneous statistical inference for response means with a control is considered in Chapter 6. An orthant test statistic is introduced. With the prior knowledge that the response means are monotone, a more efficient simultaneous confidence lower bound can be inverted from this test to detect the difference between response means and the control mean. An algorithm to compute the optimal lower bound is included. -- In Chapter 7, we demonstrate that the stepwise test procedure based on likelihood ratio test is a more efficient test procedure for detecting the minimum efficient dose in dose-response studies.
|
|---|