There are distribution functions, mean value and variance of the uniform and the triangular distributions derived in this paper. The article deals with the procedure how to get the random values above mentioned distributions from pseudo-random numbers by the inverse transformation method. The...

We propose a new class of models, transition measurement error models, to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error. We show that the response variable conditional on the error-prone...

The aim of statistical analysis and inference is to draw meaningful conclusions. In the case where there is prior knowledge of stochastic orderings or inequalities, it is desirable to incorporate this information in the estimation. This avoids possible unrealistic estimates, and may also lead to...

Statistical models involving latent variables are widely used in many areas of applications, such as biomedical science and social science. When likelihood-based parametric inferential methods are used to make statistical inference, certain distributional assumptions on the latent variables are...

Doctor of Philosophy

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...

In terms of risk measurement, probability and quantile risk estimation have developed enormously in the past decade, from value-at-risk measures to coherent measures such as expected shortfall. These measures allow an investor to determine their risk profile accounting for losses (quantiles) at...

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...