Statistics and Probability Commons^™

A Method For Finding Standard Error Estimates For Rma Expression Levels Using Bootstrap, Gabriel Nicholas

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

Oligonucleotide arrays are used in many applications. Affymetrix GeneChip arrays are widely used. Before researchers can use the information from these arrays, the raw data must be transformed and summarized into a more meaningful and usable form. One of the more popular methods for doing so is RMA (Robust Multi-array Analysis).

A problem with RMA is that the end result (estimated gene expression levels) is based on a fairly complicated process that is unusual. Specifically, there is no closed-form estimate of standard errors for the estimated gene expression levels. The current recommendation is to use a naive estimate for the …

Special Classification Models For Lichens In The Pacific Northwest, Janeen Ardito

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

A common problem in ecological studies is that of determining where to look for rare species. This paper shows how statistical models, such as classification trees, may be used to assist in the design of probability-based surveys for rare species using information on more abundant species that are associated with the rare species. This model assisted approach to survey design involves first building models for the more abundant species. The models are then used to determine stratifications for the rare species that are associated with the more abundant species. The goal of this approach is to increase the number of …

The Robustness Of Factor Analyses When The Data Does Not Conform To Standard Parametric Requirements, Haisong Peng

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

Objective: To access the robustness of factor analyses when the data does not conform to standard parametric requirements.

Methods: Data were simulated in package R. Maximum likelihood was used to fit and assess the factor models. Chi-square statistics were obtained to test hypotheses about the correct number of factors in simulated settings where the true number of factors was known. The number of true factors varied between 1 and 3; the number of observed variables was either 6 (for 1 factor) or 3 per factor for 2 or more factors.

Results: With standard normal factor populations, and normal errors added …

Optimal Path Planning And The Fast Marching Method, J. J. Clark

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

The problem of determining an optimal path for an object moving through some obstacle space presents several nontrivial subproblems. The foremost being the computational complexity that is involved and how to best deal with the associated large data volume. For example, a non-symmetric object moving in three dimensions possesses six degrees of freedom. This can lead to a computational grid that may easily be on the order of 10¹². Furthermore, for every point in the computational domain, several complex calculations must be performed. These include performing tests to determine if the object and obstacles intersect, and numerically solving …

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 …

Detection Of Changes In Financial Time Series, Rich Madsen

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

The purpose of this paper is to examine and model data from several years of foreign currency trading, to determine if one or more change points has occured in the data, and to estimate when those change points took place. Leading up to the analysis of the data we will construct and develop several statistics which we will use to determine if a change point has occured.

This paper falls into the area of computational statistics and will make use of Splus and the S+GARCH module within Splus. Heavy use will also be made of C++. The models that we …

Analysis Of A Non-Replicated Split-Split Plot Experiment, Emily Simmons Sim

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

A major obstacle in the analysis of experimental data, in many situations, is the lack of "true" or "complete" replication. In some disciplines, researchers are very aware of the importance of replication and the methods for correctly replicating an experiment. In other subject areas, however, researchers are less aware of what it means to properly replicate an experiment. Due to this lack of awareness, many non-replicated experiments are carried out every year. For many of these non-replicated experiments, there is no satisfactory statistical analysis.

The subject of this report is the analysis of two non-replicated experiments in environmental engineering. First, …

On The Model Selection In A Frailty Setting, Jill F. Lundell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

When analyzing data in a survival setting, whether of people or objects, one of the assumptions made is that the population is homogeneous. This is not true in reality and certain adjustments can be made in the model to account for heterogeneity. Frailty is one method of dealing with some of this heterogeneity. It is not possible to measure frailty directly and hence it can be very difficult to determine which frailty model is appropriate for the data in interest. This thesis investigates three model selection methods in their effectiveness at determining which frailty distribution best describes a given set …

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 …

Statistical Properties And Problems In Modeling The Bolivian Foreign Exchange Market, Gover Barja

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Bolivian foreign exchange market is explained in terms of the official and parallel exchange rates. The data covers the post hyper inflationary period from 1986 to 1992. The distribution of the rate of depreciation of the official and parallel exchange rates is long tailed and strongly departs from normality due to the existence of outliers. A market interactions model of the autoregressive kind is estimated using robust regression. This procedure produces M-parameter estimates using iteratively reweighted least squares. The robust method handles well the outlier problem and at the same time it reveals the true nature of the statistical …

Linear Operators Strongly Preserving Polynomial Equations Over Antinegative Semirings, Sang-Gu Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = X^r₁ + X^r₂ + ... + X^r_t and r₁>r₂>...>r_t≥2.

In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We …

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 …

Probability Of Discrete Failures, Weibull Distribution, Mary Jo Hansen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The intent of this research and these is to describe the development of a series of charts and tables that provide the individual and cumulative probabilities of failure applying to the Weibull statistical distribution. The mathematical relationships are developed and the computer programs are described for deterministic and Monte Carlo models that compute and verify the results. Charts and tables reflecting the probabilities of failure for a selected set of parameters of the Weibull distribution functions are provided.

Overall Life Satisfaction Of Ileostomates: Conventional Brooke Ileostomy Versus Modified Kock Pouch, Sandra Sisson Briscoe

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis is to analyze various aspects of quality of life and to determine if there is a difference in quality of life offered by a conventional ileostomy versus a continent ileostomy.

An instrument was developed to measure several factors thought to influence quality of life as well as several structural/demographic variables. This instrument was designed for persons with a conventional ileostomy and was modified for persons who had undergone conversion surgery from conventional to continent ileostomy.

Analysis of variance was performed to determine differences in quality of life for persons with a conventional, conversion, or original …

Comparison Of Bootstrap With Other Tests For Several Distributions, Yu-Yu Wong

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper discusses results of a computer simulation to investigate several different tests when sampling several distributions. The hypothesis H₀: μ=0 was tested against H₀: μ≠0, using the usual t-test, trimmed t-test, the Jackkinfe, the Bootstrap and signed-rank test. The p-values and empirical power show that the Bootstrap is as good as the t-test. The Jackknife procedure is too liberal, always obtaining small p-values. The signed-rank is a fairly good test if the data follows the Cauchy Distribution.

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 …

Nonparametric Confidence Intervals For The Reliability Of Real Systems Calculated From Component Data, Jean Spooner

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A methodology which calculates a point estimate and confidence intervals for system reliability directly from component failure data is proposed and evaluated. This is a nonparametric approach which does not require the component time to failures to follow a known reliability distribution.

The proposed methods have similar accuracy to the traditional parametric approaches, can be used when the distribution of component reliability is unknown or there is a limited amount of sample component data, are simpler to compute, and use less computer resources. Depuy et al. (1982) studied several parametric approaches to calculating confidence intervals on system reliability. The test …

A Test For Determining An Appropriate Model For Accelerated Life Data, Yuan-Who Chen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis was to evaluate a method for testing the appropriateness of accelerated life model. This method is based upon a polynomial approximation. The parameters are estimated and used for testing the appropriateness of the model.

An example illustrates the polynomial method. Real data are applied for this method. Comparison with another method demonstrates that the polynomial method is much simpler and has comparable accuracy.

A Comparison Of Rank And Bootstrap Procedures For Completely Randomized Designs With Jittering, Feng-Ling Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper discusses results of a computer simulation to investigate the effect of jittering to simulate measurement error. In addition, the classical F ratio, the bootstrap F and the F for ranked data are compared. Empirical powers and p-values suggest the bootstrap is a good and robust procedure and the rank procedure seems to be too liberal when compared to the classical F ratio.

Shamat: A Matrix Manipulation Program, Shahriyar Dadkhah

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This report is both a users guide and a programmers manual for running and modifying the program SHAMAT, an interactive matrix calculator. The program is written in Turbo Pascal version 3.0 for MS-DOS computers. This software enables the user to type in matrix equations for solving statistical problems such as multiple regression, analysis of variance, etc. All matrix operations necessary for linear models analysis are included in this program. Since each operation uses a separate subroutine, program enhancement, modification and updating is demonstrated to be easy.

Computer Program Generation Of Extreme Value Distribution Data, Stephen (Wan-Tsing) Lei

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

The application of the Monte Carlo method on the estimation in Gumbel extreme value distribution was studied. The Gumbel extreme value distribution is used to estimate the flood flow of specific return period for the design of flood mitigation project. This paper is a programming effort (1) to estimate the parameters of Gumbel distribution using the observed data and (2) to provide a random variate generating subroutine to generate random samples and order statistics of a Gumbel distribution random variable. The mean squared error is used to measure the accuracy of the estimation method. Finally, an example of the use …

Data Analysis Using Experimental Design Model Factorial Analysis Of Variance/Covariance (Dmaovc.Bas), Wesley E. Newton

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

DMAOVC.BAS is a computer program written in the compiler version of microsoft basic which performs factorial analysis of variance/covariance with expected mean squares. The program accommodates factorial and other hierarchical experimental designs with balanced sets of data. The program is writ ten for use on most modest sized microprocessors, in which the compiler is available. The program is parameter file driven where the parameter file consists of the response variable structure, the experimental design model expressed in a similar structure as seen in most textbooks, information concerning the factors (i.e. fixed or random, and the number of levels), and necessary …

Monte Carlo Simulation Of The Game Of Twenty-One, Douglas E. Loer

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

The purpose of this paper is to demonstrate the application of computer simulation to the game of Twenty-One to predict a player's expected return from the game. Twenty-One has traditionally been one of the most popular casino games and has attracted much effort to accurately estimate the house's true advantage. Probability theory has been tried, but the thousands of different combinations of cards possible in all hands throughout the entire pack make it practically impossible to apply probability theory without overlooking some possibilities. For this reason, Twenty-One is a perfect candidate for simulation. By blocking several simulations, normal theory can …

Comparison Of Bootstrap And Jacknife Statistical Procedures, Amanuel Gobena

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

This report compares the bootstrapping to jacknifing statistical procedures in terms in bias, confidence interval and estimation of median. Related literature have been reviewed. A bootstrap allows a researcher to get an approximation to the distribution of possibly complicated statistical summaries. It is based on random sampling with replacement from experimental units. Jacknife has also been in operation prior to bootstrapping statistical procedure. The jacknife divides the data into subgroups and obtains partial estimates of these subgroups by omitting one subgroup at a time. When both of these statistical resampling procedures are compared the bootstrap has less bias, more accurate …

Multiple Shooting, Monique St-Maurice

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

The purpose of this report was to study the Multiple Shooting method, a numerical method to solve boundary value ordinary differential equation. A FORTRAN program was written to solve the specific problem.

y'' = -y, y(0) = 0, y(π/2) = 1

on a microcomputer, using the microsoft FORTRAN compiler and the 8087 coprocessor.

Unbalanced Analysis Of Variance Comparing Standard And Proposed Approximation Techniques For Estimating The Variance Components, James P. Pugsley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper considers the estimation of the components of variation for a two-factor unbalanced nested design and compares standard techniques with proposed approximation procedures. Current procedures are complicated and assume the unbalanced sample size to be fixed. This paper tests some simpler techniques, assuming sample sizes are random variables. Monte Carlo techniques were used to generate data for testing of these new procedures.

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.

The Use Of Contingency Table Analysis As A Robust Technique For Analysis Of Variance, Mei-Eing Chiu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to compare Analysis of Variance with Contingency Table Analysis when the data being analyzed do not satisfy Analysis of Variance assumptions. The criteria for comparison are the powers of the Standard variance-ratio and the Chi-square test.

The test statistic and powers were obtained by Monte Carlo.

1. Calculate test statistic for each of 100 trials, this process was repeated 12 times. Each time different combination of means and variances were used.

2. Powers were obtained for each of 12 combinations of means and variances.

Whether Analysis of Variance or Contingency Table Analysis is a …

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.