Thesis (Ph. D.)--University of Wisconsin--Madison, 1985. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

by Wai-kuen Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 57). / Chapter Chapter 1 : --- Introduction --- p.1 / Chapter Chapter 2 : --- Estimation of Correlation between Censored and Polytomous Variables --- p.5 / Chapter 2.1 : --- Model --- p.5 / Chapter 2.2 : --- Maximum Likelihood Estimation between a Censored and a Polytomous Variable --- p.7 / Chapter 2.3 : --- Simulation Study --- p.14 / Chapter 2.4 : --- Extension to Several Variables --- p.18 / Chapter Chapter 3 : --- An application -- Correlation Structure Analysis --- p.33 / Chapter 3.1 : --- Model --- p.33 / Chapter 3.2 : --- Two-stage Estimation Procedure --- p.35 / Chapter 3.3 : --- Optimization Procedure --- p.37 / Chapter Chapter 4 : --- Conclusion --- p.40 / Tables --- p.42 / References --- p.57

by Tung-lok Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 57-59. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Full Maximum Likelihood Estimation of the General Model --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Model --- p.4 / Chapter 2.3 --- Identification of the model --- p.5 / Chapter 2.4 --- Maximum likelihood estimation --- p.7 / Chapter 2.5 --- Computational Procedure --- p.12 / Chapter 2.6 --- Tests of Hypothesis --- p.13 / Chapter 2.7 --- Example --- p.14 / Chapter Chapter 3 --- Bayesian Analysis of Stochastic Prior Information --- p.17 / Chapter 3.1 --- Introduction --- p.17 / Chapter 3.2 --- Bayesian Analysis of the general model --- p.18 / Chapter 3.3 --- Computational Procedure --- p.22 / Chapter 3.4 --- Test the Compatibility of the Prior Information --- p.24 / Chapter 3.5 --- Example --- p.25 / Chapter Chapter 4 --- Simulation Study --- p.27 / Chapter 4.1 --- Introduction --- p.27 / Chapter 4.2 --- Simulation1 --- p.27 / Chapter 4.3 --- Simulation2 --- p.30 / Chapter 4.4 --- Summary and Discussion --- p.31 / Chapter Chapter 5 --- Concluding Remarks --- p.33 / Tables / References --- p.57

by Yin-Ping Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 95-96). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of the Correlation between Polytomous and Interval Data --- p.6 / Chapter 2.1 --- Model --- p.6 / Chapter 2.2 --- Maximum Likelihood Estimation --- p.8 / Chapter 2.3 --- Partition Maximum Likelihood Estimation --- p.10 / Chapter 2.4 --- Optimization Procedure and Simulation Study --- p.18 / Chapter Chapter 3 --- Three-stage Procedure for Covariance Structure Analysis --- p.25 / Chapter 3.1 --- Model --- p.25 / Chapter 3.2 --- Three-stage Estimation Method --- p.26 / Chapter 3.3 --- Optimization Procedure and Simulation Study --- p.38 / Chapter Chapter 4 --- Two-stage Procedure for Correlation Structure Analysis --- p.46 / Chapter 4.1 --- Model --- p.47 / Chapter 4.2 --- Two-stage Estimation Method --- p.47 / Chapter 4.3 --- Optimization Procedure and Monte Carlo Study --- p.50 / Chapter 4.4 --- Comparison of Two Methods --- p.53 / Chapter Chapter 5 --- Conclusion --- p.56 / Tables --- p.58 / References --- p.95

by Wai-chung Lui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 76-82). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of the model with one truncated continuous variable and one polytomous variable --- p.6 / Chapter §2.1 --- The model / Chapter § 2.2 --- Likelihood function of the model / Chapter § 2.3 --- Derivatives of F (θ） / Chapter § 2.4 --- Asymptotic properties of the model / Chapter Chapter 3 --- Estimation of the model with one truncated continuous variable and several polytomous variables --- p.22 / Chapter § 3.1 --- The model / Chapter § 3.2 --- Partition Maximum Likelihood (PML) estimation / Chapter § 3.3 --- Asymptotic properties of the PML estimates / Chapter Chapter 4 --- Optimization procedures and Simulation study --- p.43 / Chapter § 4.1 --- Optimization procedures / Chapter § 4.2 --- Simulation study / Chapter Chapter 5 --- Summary and Conclusion --- p.54 / Tables --- p.56 / References --- p.76

Recently, the study of negative dependence structures has aroused considerable interest amongst researchers in actuarial science and quantitative risk management. This thesis centres on two extreme negative dependence structures in different dimensions - counter-monotonicity and mutual exclusivity, and develops their novel characterizations and applications to risk management. Bivariate random vectors are treated in the first part of the thesis, where the characterization of comonotonicity by the optimality of aggregate sums in convex order is extended to its bivariate antithesis, namely, counter-monotonicity. It is shown that two random variables are counter-monotonic if and only if their aggregate sum is minimal with respect to convex order. This defining property of counter-monotonicity is then exploited to identify a necessary and sufficient condition for merging counter-monotonic positions to be risk-reducing. In the second part, the notion of mutual exclusivity is introduced as a multi-dimensional generalization of counter-monotonicity. Various characterizations of mutually exclusive random vectors are presented, including their pairwise counter-monotonic behaviour, minimal convex sum property, and the characteristic function of their aggregate sums. These properties highlight the role of mutual exclusivity as the strongest negative dependence structure in a multi-dimensional setting. As an application, the practical problem of deriving general lower bounds on three common convex functionals of aggregate sums with arbitrary marginal distributions is considered. The sharpness of these lower bounds is characterized via the mutual exclusivity of the underlying random variables. Compared to existing bounds in the literature, the new lower bounds proposed enjoy the advantages of generality and simplicity. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

No description available.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 97-105). Also available in electronic version.

Thesis (M. Phil.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 118-122).

This thesis examines random variables of one dimension.