SCHEDULE

ABSTRACTS

Modeling Securitization Structures in the Subprime Crisis
Ambar N. Sengupta
Mathematics Department
Louisiana State University

The ongoing financial crisis originated in the collapse of the subprime mortgage market following a downturn in home values. A thorough theoretical analysis and understanding of the distinguishing features of the subprime mortgage financial structure is crucial in understanding why such a rapid and far-reaching financial crisis resulted from this particular market. In this talk we will discuss special features of subprime mortgages and their securitization vehicles. Probabilistic models used for such securitization structures, theoretical results, and results from simulations will be presented.

Generalized Inference for Weibull Distributions Based on Censored Cases
Yin Lin
Mathematics Department
University of Louisiana at Lafayette

In this presentation, we consider inferential procedures based on type I censored samples from Weibull distributions. The methods are based on the classical pivotal quantities and the concept of generalized variable approach. The procedures are exact when samples are type II censored, and they can be used as approximates for type I censored samples. The proposed methods are explained for constructing confidence intervals for a Weibull mean, quantile and for comparison of two Weibull means. The results are illustrated using some practical examples.

Bootstrap Methods for GMM Models
Mihai C. Giurcanu
Mathematics Department
University of Louisiana at Lafayette

In this paper we explore and compare the asymptotic and finite sample properties of the uniformly-weighted nonparametric bootstrap and the biased-bootstrap for generalized method of moments (GMM) models. The biased-bootstrap is a weighted bootstrap in which the weights are chosen so that the constraints implied by the GMM model hold in the sample. We prove that both the uniform and the biased-bootstrap yield consistent estimators of the sampling distribution of GMM estimator, as well as of the null distributions of Wald and likelihood-ratio GMM type tests. On the other hand, the uniform bootstrap estimator of the null distribution of J-test is inconsistent and converge in distribution to some random non-central chi-square distribution, with non-centrality parameter given by a measurable,chi-square random variable. Although the biased-bootstrap consistently estimates the null distribution of the J-test if the model holds, it has a negative impact on the local limiting power of the resulting test. We also prove in this paper that this inconsistency is resolved in both cases if the estimating equations are recentered before resampling. In addition, and in contrast to the ordinary uniform bootstrap, the parametric nature of the biased-bootstrap allows us to use importance sampling to develop an efficient bootstrap recycling algorithm for iteration of the biased-bootstrap. An empirical study on a panel data model shows the performance of different resampling schemes on small and moderate sample sizes.

A Case Study of Green Tree Frog Population Size Estimation Through Capture-Mark-Recapture Method With Individual Tagging
Nabendu Pal
Mathematics Department
University of Louisiana at Lafayette

This talk deals with estimation of a green tree frog population in a semiurban setting through repeated capture-mark-recapture method over weeks with individual tagging system which gives rise to a generalization of the well known hypergeometric distribution. Even in a simplistic situation, where it is assumed that the population remains unaffected by migration and/or mortality within a short span of time, the probability distribution of the weekly data is quite complicated. To best of our knowledge, there is no inferential method discussed on this problem in the literature. Based on the maximum likelihood estimation we adopt a parametric bootstrap approach to obtain interval estimates of the weekly population size. The method is extremely computation intensive and requires some smart programming to implement the algorithm for repeated re-sampling. Our interval estimator also shows good performance in terms of probability coverage. We also provide an approximate population estimate assuming mortality rate over a suitable interval.