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

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).

No description available.

Thesis (Ph. D.)--University of Chicago, School of Business, 2001. / Includes bibliographical references. Also available on the Internet.

published_or_final_version / Statistics / Master / Master of Philosophy

Thesis (M.S.)--Ohio University, June, 1997. / Title from PDF t.p.

Assuming a set of variates are independent and normally distributed is commonplace in statistics. In this thesis, we consider the consequences of these assumptions as they pertain to global sensitivity analysis. We begin by illustrating how the notion of sensitivity becomes distorted in the presence of codependent model inputs. This observation motivates us to develop a new methodology which accommodates for input codependencies. Our methodology can be summarized through three points: First, a new form of sensitivity is presented which performs as well as the classical form but can be obtained at a fraction of the computational cost. Second, we define a measure which quantifies the extent of distortion caused by codependent inputs. The third point is regarding the modelling of said codependencies. The multivariate normal distribution is a natural choice for modelling codependent inputs; however, our methodology uses a copula-based approach instead. Copulas are a contemporary strategy for constructing multivariate distributions whereby the marginal and joint behaviours are treated separately. As a result, a practitioner has more flexibility when modelling inputs. / Thesis (Master, Chemical Engineering) -- Queen's University, 2013-12-05 10:16:26.81