In this thesis, we study two independent samples under right censoring. Using a smoothed empirical likelihood method, we investigate the difference of quantiles in the two samples and construct the pointwise confidence intervals from it as well. The empirical log-likelihood ratio is proposed and its asymptotic limit is shown as a chi-squared distribution. In the simulation studies, in terms of coverage accuracy and average length of confidence intervals, we compare the empirical likelihood and the normal approximation method. It is concluded that the empirical likelihood method has a better performance. At last, a real clinical trial data is used for the purpose of illustration. Numerical examples to illustrate the efficacy of the method are presented.

U-statistics generalizes the concept of mean of independent identically distributed (i.i.d.) random variables and is widely utilized in many estimating and testing problems. The standard empirical likelihood (EL) for U-statistics is computationally expensive because of its onlinear constraint. The jackknife empirical likelihood method largely relieves computation burden by circumventing the construction of the nonlinear constraint. In this thesis, we adopt a new jackknife empirical likelihood method to make inference for the general volume under the ROC surface (VUS), which is one typical kind of U-statistics. Monte Carlo simulations are conducted to show that the EL confidence intervals perform well in terms of the coverage probability and average length for various sample sizes.

Researchers and publishing guidelines recommend reporting confidence intervals (CIs) not just along with null hypothesis significance testing (NHST), but for many other statistics such as effect sizes and reliability coefficients. Although CI and standard errors (SEs) are closely related, examining standard errors alone in simulation studies is not adequate because we do not always know if a standard error is small enough. Overly small SEs may lead to increased probability of Type-I error and CIs with lower coverage rate than expected. Statistical simulation studies generally examine the magnitude of the empirical standard error, but it is not clear if they examine the properties of confidence intervals. The present study examines confidence interval investigating and reporting practices, particularly with respect to coverage and bias as diagnostics in published statistical simulation studies across eight psychology journals using a systematic literature review. Results from this review will inform editorial policies and hopefully encourage researchers to report CIs.

The confidence interval estimate of percentile and its applications were studied. The three methods of estimating a confidence interval were introduced. Some properties of order statistics were reviewed. The Monte Carlo Method -- used to estimate the confidence interval was the most important one among the three methods. The generation of ordered random variables and the estimation of parameters were discussed clearly. The comparison of the three methods showed that the Monte Carlo method would always work, but the K-S and the simplified methods would not.

No description available.

<p>Subjects enrolled in a clinical trial may experience a competing risk event which alters the risk of the primary event of interest. This differs from when subject information is censored, which is non-informative. In order to calculate the cumulative incidence function (CIF) for the event of interest, competing risks and censoring must be treated appropriately; otherwise estimates will be biased. There are two commonly used methods of calculating a confidence interval (CI) for the CIF for the event of interest which account for censoring and competing risk: the Kalbfleisch-Prentice (KP) method and the Counting Process (CP) method. The goal of this paper is to understand the variances associated with the two methods to improve our understanding of the CI. This will allow for appropriate estimation of the CIF CI for a single-arm cohort study that is currently being conducted. Previous work has failed to address this question because researchers typically focus on comparing two treatment arms using statistical tests that compare cause-specific hazard functions and do not require a CI for the CIF. The two methods were compared by calculating CIs for the CIF using data from a previous related study, using bootstrapping, and a simulation study with varying event rates and competing risk rates. The KP method usually estimated a larger CIF and variance than the CP method. When event rates were low (5%), the CP method is recommended as it yields more consistent results than the KP method. The CP method is recommended for the proposed study since event rates are expected to be moderate (5-10%).</p> / Master of Science (MS)

No description available.

Ordinal coefficient alpha is a newly derived non-parametric reliability estimate. As with any point estimate, ordinal coefficient alpha is merely an estimate of a population parameter and tends to vary from sample to sample. Researchers report the confidence interval to provide readers with the amount of precision obtained. Several methods with differing computational approaches exist for confidence interval estimation for alpha, including the Fisher, Feldt, Bonner, and Hakstian and Whalen (HW) techniques. Overall, coverage rates for the various methods were unacceptably low with the Fisher method as the highest performer at 62%. Because of the poor performance across all four confidence interval methods, a need exists to develop a method which works well for ordinal coefficient alpha.

Master of Science / Department of Statistics / Paul I. Nelson / Capture-Recaputre (CR) experiments stemmed from the study of wildlife and are widely used in areas such as ecology, epidemiology, evaluation of census undercounts, and software testing, to estimate population size, survival rate, and other population parameters. The basic idea of the design is to use “overlapping” information contained in multiple samples from the population. In this report, we focus on the simplest form of Capture-Recapture experiments, namely, a two-sample Capture-Recapture design, which is conventionally called the “Petersen Method.” We study and compare the performance of three methods of constructing confidence intervals for the population size based on a Capture-Recapture design, asymptotic normality estimation, Chapman estimation, and “inverting a chi-square test” estimation, in terms of coverage rate and mean interval width. Simulation studies are carried out and analyzed using R and SAS. It turns out that the “inverting a chi-square test” estimation is better than the other two methods. A possible solution to the “zero recapture” problem is put forward. We find that if population size is at least a few thousand, two-sample CR estimation provides reasonable estimates of the population size.

Regression analysis is one of the most applied statistical techniques. The sta- tistical inference of a linear regression model with a monotone constraint had been discussed in early analysis. A natural question arises when it comes to the difference between the cases of with and without the constraint. Although the comparison be- tween confidence intervals of linear regression models with and without restriction for one predictor variable had been considered, this discussion for multiple regres- sion is required. In this thesis, I discuss the comparison of the confidence intervals between a multiple linear regression model with and without constraints.