by Wai-leung Li. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 74-77). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter § 1.1 --- Why transformation of variables in regression analysis is needed? --- p.1 / Chapter § 1.2 --- Suggested functional transformation -- Box-Cox Transformation --- p.3 / Chapter § 1.3 --- Methodology --- p.5 / Chapter § 1.4 --- General theory of constructing asymptotic confidence intervals and confidence regions --- p.9 / Chapter § 1.4.1 --- Method based on the log-likelihood ratio statistic --- p.9 / Chapter § 1.4.2 --- Method based on the asymptotic normality of the maximum likelihood estimates --- p.13 / Chapter § 1.4.3 --- Method based on the score statistic --- p.15 / Chapter § 1.5 --- General theory of constructing exact confidence intervals and confidence regions --- p.17 / Chapter § 1.6 --- Summary --- p.23 / Chapter Chapter 2 --- Confidence Intervals for the non-linear parameter λ in the Box-Cox transformation models --- p.24 / Chapter § 2.1 --- Confidence intervals based on the log-likelihood ratio statistics --- p.26 / Chapter § 2.1.1 --- Asymptotically equivalent forms for constructing confidence intervals based on the log-likelihood ratio statistics --- p.30 / Chapter § 2.2 --- Confidence intervals based on the asymptotic normality of the maximum likelihood estimates --- p.31 / Chapter § 2.3 --- Confidence intervals based on the score statistics --- p.35 / Chapter § 2.4 --- Confidence intervals based on the exact test --- p.36 / Chapter § 2.5 --- Small simulation studies of constructing confidence intervals for A based on the four different methods --- p.37 / Chapter § 2.5.1 --- Design of the simulation studies --- p.40 / Chapter § 2.5.2 --- Simulation results --- p.41 / Chapter § 2.6 --- Summary --- p.44 / Chapter Chapter 3 --- Confidence Regions for the parameters in the Box-Cox transformation models --- p.45 / Chapter § 3.1 --- Confidence regions based on the log-likelihood ratio statistics --- p.45 / Chapter § 3.1.1 --- "Confidence region for (λ,ζ1）based on the log-likelihood ratio statistics" --- p.46 / Chapter § 3.1.2 --- Confidence region for (ζ1）based on the log-likelihood ratio statistics --- p.51 / Chapter § 3.2 --- Confidence regions based on the asymptotic normality of the maximum likelihood estimates --- p.53 / Chapter § 3.2.1 --- "Confidence region for (λ,ζ1）based on the asymptotic normality of the maximum likelihood estimates" --- p.53 / Chapter § 3.2.2 --- Confidence region for (ζ1）based on the asymptotic normality of the maximum likelihood estimates --- p.57 / Chapter § 3.3 --- Confidence regions based on the score statistics --- p.58 / Chapter § 3.3.1 --- "Confidence region for (λ,ζ1） based on the score statistic" --- p.59 / Chapter § 3.3.2 --- Confidence region for (ζ1 ) based on the score statistic --- p.60 / Chapter § 3.4 --- Confidence region based on the exact test --- p.61 / Chapter § 3.5 --- Small simulation studies of constructing confidence regions for the parameters of interest based on the four different methods --- p.62 / Chapter Chapter 4 --- Robustness and Discussion --- p.67 / Chapter §4.1 --- Contamination normal distribution --- p.67 / Chapter § 4.1.1 --- Confidence intervals for the non- linear parameter λ based on the contamination normal distribution of error terms --- p.68 / Chapter § 4.1.2 --- Confidence regions for the parameters of interest based on the contamination normal distribution of the error terms --- p.70 / Chapter § 4.2 --- Summary --- p.72 / References --- p.74 / Figures / Appendix A / Appendix B / Appendix C / Appendix D
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_318238 |
| Date | January 1994 |
| Contributors | Li, Wai-leung., Chinese University of Hong Kong Graduate School. Division of Statistics. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, [8], 77, [45] leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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