Browsing by Author "Zhang, Min"

Now showing 1 - 4 of 4

Joint Distributions of Time to Default with Application to the Pricing of Credit Derivatives
(2008-05-06) Zhang, Min; Peter Bloomfield, Committee Chair; David A. Dickey, Committee Member; Jason Osborne, Committee Member; Tao Pang, Committee Member
Modeling portfolio credit risk involves the default dependencies between the individual securities in a portfolio. The copula is a common approach to construct it. It parameterizes the joint distribution of individual defaults independently of their marginal distributions. The current market standard model is the Gaussian copula. It assumes the event of default depends on both the common systematic risk factor and the individually idiosyncratic risk factor. The dependence of the defaults is induced by modeling a vector of latent variables that have a multivariate normal distribution. First we study the loss distribution of the large portfolio by using the Gaussian copula. We derive several asymptotic approximations to the loss distribution of the Gaussian copula. Every approximation is compared with the exact loss distribution by using the Hellinger distance between their probability density functions. However, the tail dependence of the extreme events such as credit defaults can not be captured by the Gaussian copula. We develop the Student's t copula process to define an appropriate dependence structure of the defaults. The dependence of the default events is induced by modeling a vector of latent variables that have a multivariate Student's t distribution. We study the loss distribution of the large portfolio by using the Student's t copula. We also derive several asymptotic approximations to the loss distribution of the Student's t copula. We compare every approximation to the exact loss distribution by using the Hellinger distance between their probability density functions. The market data of iTraxx Europe Series 4 (5-year) is investigated by using both the Gaussian copula and the Student's t copula. We say the Student's t copula works better than the Gaussian copula to describe the dependence of the extreme events with an extra parameter, the degrees of freedom of the Student's t copula. The parameters are estimated by using the weighted least squares of the mark to market. The base correlation curve implied from the Gaussian copula is skewed. The base correlation curve implied from the Student's t copula is also skewed unless we allow varying degrees of freedom. Since the implied base correlations of the individual tranches are not consistent, it is impossible to interpolate the base correlation for a non-standard tranche. A less skewed implied base correlation curve will be one of our interests in the future study.
Preventing Strength Loss of Unbleached Kraft Fibers
(2003-10-30) Zhang, Min; Samuel M. Hudson, Committee Member; Richard A. Venditti, Committee Co-Chair; John A. Heitmann, Committee Member; Martin A. Hubbe, Committee Chair
The purpose of this study was to understand the mechanism of paper strength loss that occurs when paper made from chemical pulps is recycled. It is found that due to drying, unbleached kraft pine fibers lost cellulose viscosity, water retention value, fiber flexibility and accessible surface area. Handsheets made from dried fibers had lower paper strength and lower apparent density compared to corresponding primary handsheets made from never-dried fibers. With the increase in drying temperature of virgin fibers, the above properties of dried fibers and recycled handsheets experienced larger effects. It was hypothesized that adding certain chemicals to virgin fibers before drying could prevent strength loss upon recycling. Results showed that relatively low molecular weight additives (such as sucrose and glucose) appeared to interfere with the mechanism of pore closure during drying and improved the strength of recycled paper. Higher molecular weight chemicals added to never dried virgin fibers (such as starch) also increased the strength of the recycled paper but this was attributed to residual chemical being retained on the fiber surface during recycling. Although the effect of adding certain chemicals to virgin fibers before drying could significantly prevent strength loss in recycled paper, it was determined that improvements of recycled paper strength due to refining were of much larger magnitude. It is found that recycled handsheets had lower paper strength compared with virgin handsheets at all pH values considered during paper formation within the range of pH 3 to pH 8. There was no significant effect of pH on paper strength within this range. The fiber flexibility tests showed that the method is useful to determine the flexibility of individual fibers. In the case of sugar treatment, treated fibers showed higher flexibility compared to untreated fibers after drying, and glucose was found to have larger effect than sucrose. With respect to papermaking conditions, fibers were more flexible under alkaline conditions than fibers under acidic conditions, but fibers became less flexible with increasing salt concentration and hardness.
Semiparametric Methods for Analysis of Randomized Clinical Trials and Arbitrarily Censored Time-to-event Data.
(2009-04-03) Zhang, Min; Wenbin Lu, Committee Member; Marie Davidian, Committee Chair; Anastasios A. Tsiatis, Committee Co-Chair; Daowen Zhang, Committee Member
This dissertation includes two parts. In part one, using the theory of semiparametrics, we develop a general approach to improving efficiency of nferences in randomized clinical trials using auxiliary covariates. In part two, we study "smooth" semiparametric regression analysis for arbitrarily censored time-to-event data. The primary goal of a randomized clinical trial is to make comparisons among two or more treatments. For example, in a two-arm trial with continuous response, the focus may be on the difference in treatment means; with more than two treatments, the comparison may be based on pairwise differences. With binary outcomes, pairwise odds-ratios or log-odds ratios may be used. In general, comparisons may be based on meaningful parameters in a relevant statistical model. Standard analyses for estimation and testing in this context typically are based on the data collected on response and treatment assignment only. In many trials, auxiliary baseline covariate information may also be available, and it is of interest to exploit these data to improve the efficiency of inferences. Taking a semiparametric theory perspective, we propose a broadly-applicable approach to adjustment for auxiliary covariates to achieve more efficient estimators and tests for treatment parameters in the analysis of randomized clinical trials. Simulations and applications demonstrate the performance of the methods. A general framework for regression analysis of time-to-event data subject to arbitrary patterns of censoring is proposed. The approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models, such as the baseline hazard function in the proportional hazards model, have densities satisfying mild "smoothness" conditions. Densities are approximated by a truncated series expansion that, for fixed degree of truncation, results in a "parametric" representation, which makes likelihood-based inference coupled with adaptive choice of the degree of truncation, and hence flexibility of the model, computationally and conceptually straightforward with data subject to any pattern of censoring. The formulation allows popular models, such as the proportional hazards, proportional odds, and accelerated failure time models, to be placed in a common framework; provides a principled basis for choosing among them; and renders useful extensions of the models straightforward. The utility and performance of the methods are demonstrated via simulations and by application to data from time-to-event studies.
Structured Smooth Optimization in Statistical Learning.
(2021-11-12) Zhang, Min; Eric Chi, Chair; Arvind Krishna Saibaba, Member; Minh Tang, Member; Jung-Ying Tzeng, Member