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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Nonparametric lack-of-fit tests in presence of heteroscedastic variances

Gharaibeh, Mohammed Mahmoud January 1900 (has links)
Doctor of Philosophy / Department of Statistics / Haiyan Wang / It is essential to test the adequacy of a specified regression model in order to have cor- rect statistical inferences. In addition, ignoring the presence of heteroscedastic errors of regression models will lead to unreliable and misleading inferences. In this dissertation, we consider nonparametric lack-of-fit tests in presence of heteroscedastic variances. First, we consider testing the constant regression null hypothesis based on a test statistic constructed using a k-nearest neighbor augmentation. Then a lack-of-fit test of nonlinear regression null hypothesis is proposed. For both cases, the asymptotic distribution of the test statistic is derived under the null and local alternatives for the case of using fixed number of nearest neighbors. Numerical studies and real data analyses are presented to evaluate the perfor- mance of the proposed tests. Advantages of our tests compared to classical methods include: (1) The response variable can be discrete or continuous and can have variations depend on the predictor. This allows our tests to have broad applicability to data from many practi- cal fields. (2) Using fixed number of k-nearest neighbors avoids slow convergence problem which is a common drawback of nonparametric methods that often leads to low power for moderate sample sizes. (3) We obtained the parametric standardizing rate for our test statis- tics, which give more power than smoothing based nonparametric methods for intermediate sample sizes. The numerical simulation studies show that our tests are powerful and have noticeably better performance than some well known tests when the data were generated from high frequency alternatives. Based on the idea of the Least Squares Cross-Validation (LSCV) procedure of Hardle and Mammen (1993), we also proposed a method to estimate the number of nearest neighbors for data augmentation that works with both continuous and discrete response variable.
2

Numerical comparisons of bioassay methods in estimating LC50

Zhou, Tianhong January 1900 (has links)
Master of Science / Department of Statistics / Weixing Song / The potency of a pesticide or some materials is widely studied in agricultural and biological fields. The level of a stimulus that results in a response by 50% of individuals in a population under study is an important characterizing parameter and it is denoted by the median lethal concentration (LC50) or the median lethal dose (LD50) or median. Estimation of LC50 is a type of quantal response assays that belong to qualitative indirect bioassays. In this report, seven methods of estimating LC50 are reviewed with reference to two normal distributions of tolerance in four different cases. Some modified methods are also discussed. Simulation shows that the maximum likelihood method generally outperforms all other traditional methods, if the true tolerance distribution is available. The comparison results indicate that the modified Dragstedt-Behrens method and modified Reed-Muench method are good substitutes for the original ones in most scenarios.
3

A score test of homogeneity in generalized additive models for zero-inflated count data

Nian, Gaowei January 1900 (has links)
Master of Science / Department of Statistics / Wei-Wen Hsu / Zero-Inflated Poisson (ZIP) models are often used to analyze the count data with excess zeros. In the ZIP model, the Poisson mean and the mixing weight are often assumed to depend on covariates through regression technique. In other words, the effect of covariates on Poisson mean or the mixing weight is specified using a proper link function coupled with a linear predictor which is simply a linear combination of unknown regression coefficients and covariates. However, in practice, this predictor may not be linear in regression parameters but curvilinear or nonlinear. Under such situation, a more general and flexible approach should be considered. One popular method in the literature is Zero-Inflated Generalized Additive Models (ZIGAM) which extends the zero-inflated models to incorporate the use of Generalized Additive Models (GAM). These models can accommodate the nonlinear predictor in the link function. For ZIGAM, it is also of interest to conduct inferences for the mixing weight, particularly evaluating whether the mixing weight equals to zero. Many methodologies have been proposed to examine this question, but all of them are developed under classical zero-inflated models rather than ZIGAM. In this report, we propose a generalized score test to evaluate whether the mixing weight is equal to zero under the framework of ZIGAM with Poisson model. Technically, the proposed score test is developed based on a novel transformation for the mixing weight coupled with proportional constraints on ZIGAM, where it assumes that the smooth components of covariates in both the Poisson mean and the mixing weight have proportional relationships. An intensive simulation study indicates that the proposed score test outperforms the other existing tests when the mixing weight and the Poisson mean truly involve a nonlinear predictor. The recreational fisheries data from the Marine Recreational Information Program (MRIP) survey conducted by National Oceanic and Atmospheric Administration (NOAA) are used to illustrate the proposed methodology.
4

A comparison study on the estimation in Tobit regression models

Leiker, Antoinette January 1900 (has links)
Master of Science / Department of Statistics / Weixing Song / The goal of this report is to compare various estimation procedures on regression models in which the dependent variable has a restricted range. These models, called Tobit models, are seeing an increase in use among economists and market researchers, specifically. Only the standard Tobit regression model is discussed in the report. First we will examine the five estimation methods discussed in Amemiya (1984) for standard Tobit model. These methods include Probit maximum likelihood, least squares, Heckman’s two-step, Tobit maximum likelihood, and the EM algorithm. We will examine the algorithm utilized in each method’s estimation process. We will then conduct simulation studies using these estimation procedures. Twelve scenarios have been considered consisting of three different truncation threshold on the response variable, two distributions of covariates, and the error variance known and unknown. The results are reported and a discussion of the goodness of each method follows. The study shows that the best method for estimating Tobit regression models is indeed the Tobit maximum likelihood estimation. Heckman’s two-step method and the EM algorithm also estimate these models well when the truncation rate is low and the sample size is large. The simulation results show that the Least squares estimation procedure is far less efficient than other estimation procedures.
5

An introduction to meta analysis

Boykova, Alla January 1900 (has links)
Master of Science / Department of Statistics / Dallas W. Johnson / Meta analysis is a statistical technique for synthesizing of results obtained from multiple studies. It is the process of combining, summarizing, and reanalyzing previous quantitative research. It yields a quantitative summary of the pooled results. Decisions of the validity of a hypothesis cannot be based on the results of a single study, because results typically vary from one study to the next. Traditional methods do not allow involving more than a few studies. Meta analysis provides certain procedures to synthesize data across studies. When the treatment effect (or effect size) is consistent from one study to the next, meta-analysis can be used to identify this common effect. When the effect varies from one study to the next, meta-analysis may be used to identify the reason for the variation. The amount of accumulated information in fast developing fields of science such as biology, medicine, education, pharmacology, physics, etc. increased very quickly after the Second World War. This lead to large amounts of literature which was not systematized. One problem in education might include ten independent studies. All of the studies might be performed by different researchers, using different techniques, and different measurements. The idea of integrating the research literature was proposed by Glass (1976, 1977). He referred it as the meta analysis of research. There are three major meta analysis approaches: combining significance levels, combining estimates of effect size for fixed effect size models and random effect size models, and vote-counting method.
6

A simple univariate outlier identification procedure on ratio data collected by the Department of Revenue for the state of Kansas

Jun, Hyoungjin January 1900 (has links)
Master of Science / Department of Statistics / John E. Boyer Jr / In order to impose fair taxes on properties, it is required that appraisers annually estimate prices of all the properties in each of the counties in Kansas. The Department of Revenue of Kansas oversees the quality of work of appraisers in each county. The Department of Revenue uses ratio data which is appraisal price divided by sale price for those parcels which are sold during the year as a basis for evaluating the work of the appraisers. They know that there are outliers in these ratio data sets and these outliers can impact their evaluations of the county appraisers. The Department of Revenue has been using a simple box plot procedure to identify outliers for the previous 10 years. Staff members have questioned whether there might be a need for improvement in the procedure. They considered the possibility of tuning the procedure to depend on distributions and sample sizes. The methodology as a possible solution was suggested by Iglewicz et al. (2007). In this report, we examine the new methodology and attempt to apply it to ratio data sets provided by the Department of Revenue.
7

Modeling a frost index in Kansas, USA

Wang, Yang January 1900 (has links)
Master of Science / Department of Statistics / Perla Reyes Cuellar / A frost index is a calculated value that can be used to describe the state and the changes in the weather conditions. Frost indices affect not only natural and managed ecosystems, but also a variety of human activities. In addition, they could indicate changes in extreme weather and climate events. Growing season length is one of the most important frost indices. In this report, growing season lengths were collected from 23 long-term stations over Kansas territory. The records extended to the late 1800s for a few stations, but many started observations in the early 1900s. Though the start dates of the records were different, the end dates were the same (2009). To begin with, time series models of growing season length for all the stations were fitted. In addition, by using fitted time series models, predictions and validation checking were conducted. Then a regular linear regression model was fitted for the GSL data. It removed the temporal trend by doing regression on year and it showed us the relationship between GSL and elevation. Finally, based on a penalized likelihood method with least angle regression (LARS) algorithm, spatial-temporal model selection and parameter estimation were performed simultaneously. Different neighborhood structures were used for model fitting. The spatial-temporal linear regression model obtained was used for interpreting growing season length of those stations across Kansas. These models could be used for agricultural management decision-making and updating recommendations for planting date in Kansas area.
8

Confidence intervals on several functions of the components of variance in a one-way random effects experiment

Banasik, Aleksandra Anna January 1900 (has links)
Master of Science / Department of Statistics / Dallas E. Johnson / Variability is inherent in most data and often it is useful to study the variability so scientists are able to make more accurate statements about their data. One of the most popular ways of analyzing variance in data is by making use of a one-way ANOVA which consists of partitioning the variability among observations into components of variability corresponding to between groups and within groups. One then has σ(subY)(superscript 2)=σ (sub A) (superscript)2+σ(sub e)(superscript 2). Thus there are two variance components. In certain situations, in addition to estimating these components of variance, it is important to estimate functions of the variance components. This report is devoted to methods for constructing confidence intervals for three particular functions of variance components in the unbalanced One- way random effects models. In order to compare the performance of the methods, simulations were conducted using SAS® and the results were compared across several scenarios based on the number of groups, the number of observations within each group, and the value of sigma (sub A)(superscript 2).
9

A simulation evaluation of backward elimination and stepwise variable selection in regression analysis

Li, Xin January 1900 (has links)
Master of Science / Department of Statistics / Paul Nelson / A first step in model building in regression analysis often consists of selecting a parsimonious set of independent variables from a pool of candidate independent variables. This report uses simulation to study and compare the performance of two widely used sequential, variable selection algorithms, stepwise and backward elimination. A score is developed to assess the ability of any variable selection method to terminate with the correct model. It is found that backward elimination performs slightly better than stepwise, increasing sample size leads to a relatively small improvement in both methods and that the magnitude of the variance of the error term is the major factor determining the performance of both.
10

Determining the effectiveness of including spatial information into a nematode/nutsedge pest complex model

Vetter, Joel January 1900 (has links)
Master of Science / Department of Statistics / Leigh Murray / An experiment was performed in 2005-2006 to determine if the variety of an alfalfa (Medicago sativa) crop rotation can effectively reduce the pest complex consisting of the yellow and purple nutsedge (YNS & PNS) weeds and the southern root-knot nematode (SRKN). During the 2005-2006 growing season, six months were selected to take samples from the alfalfa field (three months in 2005 and three months in 2006). The field was divided into 1m x 2m quadrats. Each month eighty quadrats were randomly selected. The counts of PNS, YNS and a soil sample (analyzed for the count of juvenile SRKN) were taken from each quadrat. In this study, two different ways were examined use [i.e. using] spatial information provided from the experiment to alter the original model. First spatial information was treated as fixed effects. Second spatial information was treated as random effects by modifying the residual variance matrix using various “spatial” variance-covariance structures. The results were compared to the original Poisson model and the spatial models to each other but did not have an effective way of comparing random effects models with the fixed effects models. For this data, the use of spatial statistics did not improve the original model consistently. This may be partly because of the nature of the experiment. The alfalfa effectively reduced the YNS, PNS, and SRKN counts. The spatial information was generally more useful earlier in the experiment when the YNS, PNS, and SRKN populations were denser.

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