Physical Sciences and Mathematics Commons^™

Bayesian Estimation Of The Intensity Function Of A Non-Homogeneous Poisson Process, James Jensen

Theses

In this paper we explore Bayesian inference and its application to the problem of estimating the intensity function of a non-homogeneous Poisson process. These processes model the behavior of phenomena in which one or more events, known as arrivals, occur independently of one another over a certain period of time. We are concerned with the number of events occurring during particular time intervals across several realizations of the process. We show that given sufficient data, we are able to construct a piecewise-constant function which accurately estimates the mean rates on particular intervals. Further, we show that as we reduce these …

Estimation Problems For Pooled Data, Xichen Mou

Theses and Dissertations

In epidemiological applications, individual specimens (e.g., blood, urine, etc.) are often pooled together to detect the presence of disease or to measure the concentration level of a specific biomarker. Due to the advantage of cost efficiency, pooled data are also seen in diverse areas such as genetics, animal ecology, and environmental science. With pooled data, individual observations are masked and new statistical methods are needed to estimate characteristics such as disease prevalence, the underlying density function of a biomarker, etc. We focus on three estimation problems for pooled data. Chapters 2 and 3 propose nonparametric estimators for the density function …

Exploring The Variance Of The Sample Variance Through Estimation And Simulation, Christina Stradwick

Theses, Dissertations and Capstones

In this thesis, we examine properties of the variance of the sample variance, which we will denote V (S ² ). We derive a formula for this variance and show that it only depends on the sample size, variance, and kurtosis of the underlying distribution. We also derive the maximum likelihood estimators for this parameter, V^ˆ (S ² ), under the normal, exponential, Bernoulli, and Poisson distributions and end the thesis with simulations demonstrating the distributions of these estimators.

Fitting A Complex Markov Chain Model For Firm And Market Productivity, Julia Ruth Valder

Theses and Dissertations

This thesis develops a methodology of estimating parameters for a complex Markov chain model for firm productivity. The model consists of two Markov chains, one describing firm-level productivity and the other modeling the productivity of the whole market. If applicable, the model can be used to help with optimal decision making problems for labor demand. The need for such a model is motivated and the economical background of this research is shown. A brief introduction to the concept of Markov chains and their application in this context is given. The simulated data that is being used for the estimation is …

Strategies To Adjust For Response Bias In Clinical Trials: A Simulation Study, Victoria R. Swaidan

USF Tampa Graduate Theses and Dissertations

Background: Response bias can distort treatment effect estimates and inferences in clinical trials. Although prevention, quantification, and adjustments have been developed, current methods are not applicable when subject-level reliability is used as the measure of response bias. Thus, the objective of the current study is to develop, test, and recommend a series of bias correction strategies for use in these cases. Methods: Monte Carlo simulation and logistic regression modeling were used to develop the strategies, examining the collective impact of sample size (N), effect size (ES), reliability distribution, and response style on estimating the treatment effect size in a series …

Dimension Reduction For Classification With Many Covariates And Pathway Activity Level Estimation, Seungchul Baek

Theses and Dissertations

The development of science and technology has enabled the use of more covariates. As a result, it has become more difficult to identify dependencies among many covariates. Dimension reduction provides an efficient way to handle this issue by summarizing the effect of covariates via a few linear combinations of covariates. In this dissertation, two methodologies for real-life problems are provided by using dimension reduction equipped with semiparametric theory. The use of semiparametrics allows maximal flexibility of the model by letting some features of the model completely unspecified, while we still enjoy the interpretability of the model through estimating the parameters …

Semiparametric Statistical Estimation And Inference With Latent Information, Qianqian Wang

Theses and Dissertations

In Chapter 1, we predicted disease risk by transformation models in the presence of missing subgroup identifiers. When a discrete covariate defining subgroup membership is missing for some of the subjects in a study, the distribution of the outcome follows a mixture distribution of the subgroup-specific distributions. Taking into account the uncertain distribution of the group membership and the covariates, we model the relation between the disease onset time and the covariates through transformation models in each sub-population, and develop a nonparametric maximum likelihood based estimation implemented through EM algorithm along with its inference procedure. We further propose methods to …

Sample Size Estimation For Linear Mixed Models With Dependent End Points, Michael Nsiah-Nimo

Open Access Theses & Dissertations

The primary objective is sample size estimation in linear mixed model settings. Sample size estimation is an important component of planning a well thought out scientific experiment. Whenever sample size estimation is performed, taking into account a priori model based inferences will provide a sample size estimate that will achieve the desired power without inflating the type I error rate of the study.

One common practice is a traditional approach cited in the literature that uses the largest sample size after you Bonferroni the type I error rate to estimate sample sizes as such. We are going to take into …

Juvenile Remains: Predicting Body Mass And Stature In Modern American Populations, Erin F E Pinkston

Cal Poly Humboldt theses and projects

There are increasing numbers of unidentified persons in the U.S. and abroad. To generate positive identifications, forensic anthropologists and others working in the medicolegal field employ a variety of methods to produce biological profiles to match to case files and missing persons databases. Body mass, and stature are two important components of a biological profile, and both can be estimated using regression formulae derived from skeletal metrics. In cases of unidentified juvenile remains, these are particularly important metrics, as it is difficult or impossible to determine sex in prepubescent remains, and the quality of ancestry estimation is currently under debate …

Estimation Problems In Complex Field Studies With Deep Interactions: Time-To-Event And Local Regression Models For Environmental Effects On Vital Rates, Krzysztof M. Sakrejda

Doctoral Dissertations

Field studies that measure vital rates in context over extended time periods are a cornerstone of our understanding of population processes. These studies inform us about the relationship between biological process and environmental noise in an irreplaceable way. These data sets bring ``big data'' and ``big model'' challenges, which limit the application of standard software (e.g., \textbf{BUGS}). The environmental sensitivity of vital rates is also expected to exhibit interactions and non-linearity, which typically result in difficult model selection questions in large data sets. Finally, long-term ecological data sets often contain complex temporal structure. In commonly applied discrete-time models complex temporal …

Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation, Araz Ryan Hashemi

Wayne State University Dissertations

This dissertation investigates problems arising in identification and control of stochastic systems. When the parameters determining the underlying systems are unknown and/or time varying, estimation and adaptive filter- ing are invoked to to identify parameters or to track time-varying systems. We begin by considering linear systems whose coefficients evolve as a slowly- varying Markov Chain. We propose three families of constant step-size (or gain size) algorithms for estimating and tracking the coefficient parameter: Least-Mean Squares (LMS), Sign-Regressor (SR), and Sign-Error (SE) algorithms.

The analysis is carried out in a multi-scale framework considering the relative size of the gain (rate of …

The Quotient Of The Beta-Weibull Distribution, Nonhle Channon Mdziniso

Theses, Dissertations and Capstones

A new class of distributions recently developed involves the logit of the beta distribution. Among this class of distributions are, the beta-Normal (Eugene et al. [15]); beta-Gumbel (Nadarajah and Kotz [18]); beta-Exponential (Nadarajah and Kotz [19]); beta-Weibull (Famoye et al. [6]); beta-Rayleigh (Akinsete and Lowe [3]); beta-Laplace (Kozubowshi and Nadarajah [20]); and beta-Pareto (Akinsete et al. [4]), among a few others. Many useful statistical properties arising from these distributions and their applications to real life data have been discussed in literature. One approach by which a new statistical distribution is generated is by the transformation of random variables having known …

Statistical Methods For Nonlinear Dynamic Models With Measurement Error Using The Ricker Model, David Joseph Resendes

Open Access Dissertations

In ecological population management, years of animal counts are fit to nonlinear, dynamic models (e.g. the Ricker model) because the values of the parameters are of interest. The yearly counts are subject to measurement error, which inevitably leads to biased estimates and adversely affects inference if ignored. In the literature, often convenient distribution assumptions are imposed, readily available estimated measurement error variances are not utilized, or the measurement error is ignored entirely. In this thesis, ways to estimate the parameters of the Ricker model and perform inference while accounting for measurement error are investigated where distribution assumptions are minimized and …

Statistical Properties Of A Convoluted Beta-Weibull Distribution, Jianan Sun

Theses, Dissertations and Capstones

A new class of distributions recently developed involves the logit of the beta distribution. Among this class of distributions are the beta-normal (Eugene et.al. (2002)); beta-Gumbel (Nadarajah and Kotz (2004)); beta-exponential (Nadarajah and Kotz (2006)); beta-Weibull (Famoye et al. (2005)); beta-Rayleigh (Akinsete and Lowe (2008)); beta-Laplace (Kozubowski and Nadarajah (2008)); and beta-Pareto (Akinsete et al. (2008)), among a few others. Many useful statistical properties arising from these distributions and their applications to real life data have been discussed in the literature. One approach by which a new statistical distribution is generated is by the transformation of random variables having known …

On The Testing And Estimation Of High-Dimensional Covariance Matrices, Thomas Fisher

All Dissertations

Many applications of modern science involve a large number of parameters. In
many cases, the number of parameters, p, exceeds the number of observations,
N. Classical multivariate statistics are based on the assumption that the
number of parameters is fixed and the number of observations is large. Many of
the classical techniques perform poorly, or are degenerate, in high-dimensional
situations.
In this work, we discuss and develop statistical methods for inference of
data in which the number of parameters exceeds the number of observations.
Specifically we look at the problems of hypothesis testing regarding and the
estimation of the covariance …

Sensitivity To Distributional Assumptions In Estimation Of The Odp Thresholding Function, Wendy Jill Bunn

Theses and Dissertations

Recent technological advances in fields like medicine and genomics have produced high-dimensional data sets and a challenge to correctly interpret experimental results. The Optimal Discovery Procedure (ODP) (Storey 2005) builds on the framework of Neyman-Pearson hypothesis testing to optimally test thousands of hypotheses simultaneously. The method relies on the assumption of normally distributed data; however, many applications of this method will violate this assumption. This thesis investigates the sensitivity of this method to detection of significant but nonnormal data. Overall, estimation of the ODP with the method described in this thesis is satisfactory, except when the nonnormal alternative distribution has …

Generalized Minimum Penalized Hellinger Distance Estimation And Generalized Penalized Hellinger Deviance Testing For Generalized Linear Models: The Discrete Case, Huey Yan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation, robust and efficient alternatives to quasi-likelihood estimation and likelihood ratio tests are developed for discrete generalized linear models. The estimation method considered is a penalized minimum Hellinger distance procedure that generalizes a procedure developed by Harris and Basu for estimating parameters of a single discrete probability distribution from a random sample. A bootstrap algorithm is proposed to select the weight of the penalty term. Simulations are carried out to compare the new estimators with quasi-likelihood estimation. The robustness of the estimation procedure is demonstrated by simulation work and by Hapel's α-influence curve. Penalized minimum Hellinger deviance tests …

Adaptive Density Estimation Based On The Mode Existence Test, Nizar Sami Jawhar

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The kernel persists as the most useful tool for density estimation. Although, in general, fixed kernel estimates have proven superior to results of available variable kernel estimators, Minnotte's mode tree and mode existence test give us newfound hope of producing a useful adaptive kernel estimator that triumphs when the fixed kernel methods fail. It improves on the fixed kernel in multimodal distributions where the size of modes is unequal, and where the degree of separation of modes varies. When these latter conditions exist, they present a serious challenge to the best of fixed kernel density estimators. Capitalizing on the work …

A Comparison Of Estimation Procedures For The Beta Distribution, Huey Yan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The beta distribution may be used as a stochastic model for continuous proportions in many situations in applied statistics. This thesis was concerned with estimation of the parameters of the beta distribution in three different situations.

Three different estimation procedures-the method of moments, maximum likelihood, and a hybrid of these two methods, which we call the one-step improvement-were compared by computer simulation, for beta data and beta data contaminated by zeros and ones. We also evaluated maximum likelihood estimation in the context of censored data, and Newton's method as a numerical procedure for solving the likelihood equations …

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.

Parameter Estimation For Generalized Pareto Distribution, Der-Chen Lin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The generalized Pareto distribution was introduced by Pickands (1975). Three methods of estimating the parameters of the generalized Pareto distribution were compared by Hosking and Wallis (1987). The methods are maximum likelihood, method of moments and probability-weighted moments.

An alternate method of estimation for the generalized Pareto distribution, based on least square regression of expected order statistics (REOS), is developed and evaluated in this thesis. A Monte Carlo comparison is made between this method and the estimating methods considered by Hosking and Wallis (1987). This method is shown to be generally superior to the maximum likelihood, method of moments and …

Estimation In Truncated Exponential Family Of Distributions, Laxman M. Hegde

Mathematics & Statistics Theses & Dissertations

Estimating the parameters of a truncated distribution is a well known problem in statistical inference. The non-existence of the maximum likelihood estimator (m.l.e.) with positive probability in certain truncated distributions is not well known. To mention a few results in the literature:

(i) Deemer and Votaw 1955 show that the maximum likelihood estimator does not exist in a truncated negative exponential distribution on 0,T , T > 0 known, whenever the sample mean x (GREATERTHEQ) T/2.

(ii) Broeder 1955 shows that the maximum likelihood estimator of the scale parameter of a truncated gamma distribution, with the shape parameter being known, becomes …

Correction Of Bias In Estimating Autocovariance Function, Len-Hong Wu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis was to evaluate a method for reducing the bias of estimation for autocovariance estimators. Two methods are compared, one is the standard method and the other is an adjustment method. The Monte Carlo method is used within comparison.

The bias and the mean squared error of the estimated autocovariance is computed for several time series models and two variations of the adjustment method of estimation. The results indicate some improvement in bias and mean squared error for the new method.

Least Squares Estimation Of The Pareto Type I And Ii Distribution, Ching-Hua Chien

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The estimation of the Pareto distribution can be computationally expensive and the method is badly biased. In this work, an improved Least Squares derivation is used and the estimation will be less biased. Numerical examples and figures are provided so that one may observe the solution more clearly. Furthermore, by varying the different methods of estimation, a comparing of the estimators of the parameters is given. The improved Least Squares derivation is confidently employed for it is economic and efficient.

Parameter Estimation In Nonstationary M/M/S Queueing Models, Pensri Vajanaphanich

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

If either the arrival rate or the service rate in an M/M/S queue exhibit variability over time, then no steady state solution is available for examining the system behavior. The arrival and service rates can be represented through Fourier series approximations. This permits numerical approximation of the system characteristics over time.

An example of an M/M/S representation of the operations of emergency treatment at Logan Regional hospital is presented. It requires numerical integration of the differential equation for L(t), the expected number of customers in the system at time t.

Estimation Of Floods When Runoff Originates From Nonhomogeneous Sources, David Ray Olson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Extreme value theory is used as a basis for deriving a distribution function for flood frequency analysis when runoff originates from nonhomogeneous sources. A modified least squares technique is used to estimate the parameters of the distribution function for eleven rivers. Goodness-of-fit statistics are computed and the distribution function is found to fit the data very well.

The derived distribution function is recommended as a base method for flood frequency analysis for rivers exhibiting nonhomogeneous sources of runoff if further investigation also proves to be positive.

A Discussion Of An Empirical Bayes Multiple Comparison Technique, Donna Baranowski

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This paper considers the application and comparison of Bayesian and nonBayesian multiple comparison techniques applied to sets of chemical analysis data. Suggestions are also made as to which methods should be used.

Multicollinearity And The Estimation Of Regression Coefficients, John Charles Teed

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The precision of the estimates of the regression coefficients in a regression analysis is affected by multicollinearity. The effect of certain factors on multicollinearity and the estimates was studied. The response variables were the standard error of the regression coefficients and a standarized statistic that measures the deviation of the regression coefficient from the population parameter.

The estimates are not influenced by any one factor in particular, but rather some combination of factors. The larger the sample size, the better the precision of the estimates no matter how "bad" the other factors may be.

The standard error of the regression …

Estimation Of Μy Using The General Regression Model (In Sampling), Michael R. Manieri

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The methods of ratio and regression estimators discussed by Cochran(l977) are given as background materials and extended to the estimation of µy, the population mean of the Y's, using a general regression model.

The propagation of error technique given by Deming(l948) is used as an approximation to find the variance of the estimator µy.

Examples are given for each of the various models. Variances of μy are calculated and compared

A Comparative Analysis Of The Use Of A Markov Chain Versus A Binomial Probability Model In Estimating The Probability Of Consecutive Rainless Days, Jack Wilfred Homeyer

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Markov chain process for predicting the occurence of a sequence of rainless days, a standard technique, is critically examined in light of the basic underlying assumptions that must be made each time it is used. This is then compared to a simple binomial model wherein an event is defined to be a series of rainless days of desired length. Computer programs to perform the required calculations are then presented and compared as to complexity and operating characteristics. Finally, an example of applying both programs to real data is presented and further comparisons are drawn between the two techniques.