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EXPLORING CONFIDENCE INTERVALS IN THE CASE OF BINOMIAL AND HYPERGEOMETRIC DISTRIBUTIONS
Title
EXPLORING CONFIDENCE INTERVALS IN THE CASE OF BINOMIAL AND HYPERGEOMETRIC DISTRIBUTIONS.
Creator
Mojica, Irene, Pensky, Marianna, University of Central Florida
Abstract / Description
The objective of this thesis is to examine one of the most fundamental and yet important methodologies used in statistical practice, interval estimation of the probability of success in a binomial distribution. The textbook confidence interval for this problem is known as the Wald interval as it comes from the Wald large sample test for the binomial case. It is generally acknowledged that the actual coverage probability of the standard interval is poor for values of p near 0 or 1. Moreover,...
Show moreThe objective of this thesis is to examine one of the most fundamental and yet important methodologies used in statistical practice, interval estimation of the probability of success in a binomial distribution. The textbook confidence interval for this problem is known as the Wald interval as it comes from the Wald large sample test for the binomial case. It is generally acknowledged that the actual coverage probability of the standard interval is poor for values of p near 0 or 1. Moreover, recently it has been documented that the coverage properties of the standard interval can be inconsistent even if p is not near the boundaries. For this reason, one would like to study the variety of methods for construction of confidence intervals for unknown probability p in the binomial case. The present thesis accomplishes the task by presenting several methods for constructing confidence intervals for unknown binomial probability p. It is well known that the hypergeometric distribution is related to the binomial distribution. In particular, if the size of the population, N, is large and the number of items of interest k is such that k/N tends to p as N grows, then the hypergeometric distribution can be approximated by the binomial distribution. Therefore, in this case, one can use the confidence intervals constructed for p in the case of the binomial distribution as a basis for construction of the confidence intervals for the unknown value k = pN. The goal of this thesis is to study this approximation and to point out several confidence intervals which are designed specifically for the hypergeometric distribution. In particular, this thesis considers several confidence intervals which are based on estimation of a binomial proportion as well as Bayesian credible sets based on various priors.
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Date Issued
2011
Identifier
CFE0003919, ucf:48740
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0003919
PARAMETER ESTIMATION IN LINEAR REGRESSION
Title
PARAMETER ESTIMATION IN LINEAR REGRESSION.
Creator
Ollikainen, Kati, Malone, Linda, University of Central Florida
Abstract / Description
Today increasing amounts of data are available for analysis purposes and often times for resource allocation. One method for analysis is linear regression which utilizes the least squares estimation technique to estimate a model's parameters. This research investigated, from a user's perspective, the ability of linear regression to estimate the parameters' confidence intervals at the usual 95% level for medium sized data sets. A controlled environment using simulation with known...
Show moreToday increasing amounts of data are available for analysis purposes and often times for resource allocation. One method for analysis is linear regression which utilizes the least squares estimation technique to estimate a model's parameters. This research investigated, from a user's perspective, the ability of linear regression to estimate the parameters' confidence intervals at the usual 95% level for medium sized data sets. A controlled environment using simulation with known data characteristics (clean data, bias and or multicollinearity present) was used to show underlying problems exist with confidence intervals not including the true parameter (even though the variable was selected). The Elder/Pregibon rule was used for variable selection. A comparison of the bootstrap Percentile and BCa confidence interval was made as well as an investigation of adjustments to the usual 95% confidence intervals based on the Bonferroni and Scheffe multiple comparison principles. The results show that linear regression has problems in capturing the true parameters in the confidence intervals for the sample sizes considered, the bootstrap intervals perform no better than linear regression, and the Scheffe method is too wide for any application considered. The Bonferroni adjustment is recommended for larger sample sizes and when the t-value for a selected variable is about 3.35 or higher. For smaller sample sizes all methods show problems with type II errors resulting from confidence intervals being too wide.
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Date Issued
2006
Identifier
CFE0001482, ucf:47081
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001482
APPLICATION OF STATISTICAL METHODS IN RISK AND RELIABILITY
Title
APPLICATION OF STATISTICAL METHODS IN RISK AND RELIABILITY.
Creator
Heard, Astrid, Pensky, Marianna, University of Central Florida
Abstract / Description
The dissertation considers construction of confidence intervals for a cumulative distribution function F(z) and its inverse at some fixed points z and u on the basis of an i.i.d. sample where the sample size is relatively small. The sample is modeled as having the flexible Generalized Gamma distribution with all three parameters being unknown. This approach can be viewed as an alternative to nonparametric techniques which do not specify distribution of X and lead to less efficient procedures....
Show moreThe dissertation considers construction of confidence intervals for a cumulative distribution function F(z) and its inverse at some fixed points z and u on the basis of an i.i.d. sample where the sample size is relatively small. The sample is modeled as having the flexible Generalized Gamma distribution with all three parameters being unknown. This approach can be viewed as an alternative to nonparametric techniques which do not specify distribution of X and lead to less efficient procedures. The confidence intervals are constructed by objective Bayesian methods and use the Jeffreys noninformative prior. Performance of the resulting confidence intervals is studied via Monte Carlo simulations and compared to the performance of nonparametric confidence intervals based on binomial proportion. In addition, techniques for change point detection are analyzed and further evaluated via Monte Carlo simulations. The effect of a change point on the interval estimators is studied both analytically and via Monte Carlo simulations.
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Date Issued
2005
Identifier
CFE0000736, ucf:46565
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0000736
APPLICATION OF THE EMPIRICAL LIKELIHOOD METHOD IN PROPORTIONAL HAZARDS MODEL
Title
APPLICATION OF THE EMPIRICAL LIKELIHOOD METHOD IN PROPORTIONAL HAZARDS MODEL.
Creator
HE, BIN, Ren, Jian-Jian, University of Central Florida
Abstract / Description
In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment...
Show moreIn survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) approach to construct goodness-of-fit test and provide estimates for the Cox model with various types of censored data.Specifically, the problems under consideration are the two-sample Cox model and stratified Cox model with right censored data, doubly censored data and partly interval-censored data. Related computational issues are discussed, and some simulation results are presented. The procedures developed in the work are applied to several real data sets with some discussion.
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Date Issued
2006
Identifier
CFE0001099, ucf:46780
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001099