In the study of finance, likelihood based or moment based methods are frequently used to estimate parameters for various kinds of models given the sampled return data. While the former method is not robust, the latter one suffers from loss of efficiency and high noise-to-signal ratio in the...

This thesis focuses on two statistical problems related to credit scoring. In credit scoring of individuals, two classes are distinguished, namely low and high risk individuals (the so-called "good" and "bad" risk classes). Firstly, we suggest a measure which may be used to study the nature of a...

The lognormal distribution is useful in modeling continuous random variables which are greater than or equal to zero. Example scenarios in which the lognormal distribution is used include, among many others: in medicine, latent periods of infectious diseases; in environmental science, the...

The beta distribution is useful in modeling continuous random variables that lie between 0 and 1, such as proportions and percentages. The beta distribution takes on many different shapes and may be described by two shape parameters, alpha and beta, that can be difficult to estimate. Maximum...

This dissertation consists of three essays on modeling and parameter estimation for covariance non-stationary processes. The first essay considers the non-linear deformation of time scale for G(lambda)-stationary processes developed by Jiang, Gray and Woodward [2006]. After the appropriate...

We consider the problem of model assessment by risk estimation. Variousapproaches to risk estimation are considered in a uni ed framework. This a discussion of various complexity dimensions and approaches to obtainingbounds on covering numbers is also presented.The second type of training sample...

Previous research implementing stratification on the propensity score has generally relied on using five strata, based on prior theoretical groundwork and minimal empirical evidence as to the suitability of quintiles to adequately reduce bias in all cases and across all sample sizes. This study...

To overcome the curse of dimensionality, dimension reduction is important andnecessary for understanding the underlying phenomena in a variety of fields.Dimension reduction is the transformation of high-dimensional data into ameaningful representation in the low-dimensional space. It can be...

This thesis is concerned with simulation output analysis. In particular, we are inter-ested in estimating the variance parameter of a steady-state output process. The estimationof the variance parameter has immediate applications in problems involving (i) the precisionof the sample mean as a...