Sigmoid curves have found broad applicability in biological sciences and biopharmaceutical research during the last decades. A well planned experiment design is essential to accurately estimate the parameters of the model. In contrast to a large literature and extensive results on optimal designs for linear models, research on the design for nonlinear, including sigmoid curve, models has not kept pace. Furthermore, most of the work in the optimal design literature for nonlinear models concerns the characterization of minimally supported designs. These minimal, optimal designs are frequently criticized for their inability to check goodness of fit, as there are no additional degrees of freedom for the testing. This design issue can be a serious problem, since checking the model adequacy is of particular importance when the model is selected without complete certainty. To assess for lack of fit, we must add at least one extra distinct design point to the experiment. The goal of this dissertation is to identify optimal or highly efficient designs capable of checking the fit for sigmoid curve models. In this dissertation, we consider some commonly used sigmoid curves, including logistic, probit and Gompertz models with two, three, or four parameters. We use D-optimality as our design criterion. We first consider adding one extra point to the design, and consider five alternative designs and discuss their suitability to test for lack of fit. Then we extend the results to include one more additional point to better understand the compromise among the need of detecting lack of fit, maintaining high efficiency and the practical convenience for the practitioners. We then focus on the two-parameter Gompertz model, which is widely used in fitting growth curves yet less studied in literature, and explore three-point designs for testing lack of fit under various error variance structures. One reason that nonlinear design problems are so challenging is that, with nonlinear models, information matrices and optimal designs depend on the unknown model parameters. We propose a strategy to bypass the obstacle of parameter dependence for the theoretical derivation. This dissertation also successfully characterizes many commonly studied sigmoid curves in a generalized way by imposing unified parameterization conditions, which can be generalized and applied in the studies of other sigmoid curves. We also discuss Gompertz model with different error structures in finding an extra point for testing lack of fit. / Statistics

殖利率曲線為描述零息債卷的殖利率與其到期日間之關係，一般來說其形狀應為正斜率，而一旦殖利率曲線反轉而呈現負斜率時，許多人將之解讀為未來經濟即將走弱的訊號。本論文主要是以Probit Model呈現期間利差與重貼現率的預測能力，並將結果區分為樣本內與樣本外呈現。實證結果發現，與國外文獻比較起來，台灣殖利率曲線斜率捕捉景氣蕭條的能力遜色許多，可能與兩國在經濟體質或是央行政策執行依據上的不同有關。而相較於殖利率曲線的斜率，重貼現率對於台灣景氣的影響更為明顯，顯示出台灣的經濟深受央行政策影響。而不論是在樣本內或樣本外的結果方面，皆顯示期間利差搭配重貼現率的預測能力會較只有期間利差單一解釋變數時來的好。

A common problem in regression analysis is that some covariates are measured with errors. In this dissertation we present simulation-based approach to estimation in two popular regression models with a categorical response variable and classical measurement errors in covariates. The first model is the regression model with a binary response variable. The second one is the proportional odds regression with an ordinal response variable. In both regression models we consider method of moments estimators for therein unknown parameters that are defined via minimizing respective objective functions. The later functions involve multiple integrals and make obtaining of such estimators unfeasible. To overcome this computational difficulty, we propose Simulation-Based Estimators (SBE). This method does not require parametric assumptions for the distributions of the unobserved covariates and error components. We prove consistency and asymptotic normality of the proposed SBE's under some regularity conditions. We also examine the performance of the SBE's in finite-sample situations through simulation studies and two real data sets: the data set from the AIDS Clinical Trial Group (ACTG175) study for our logistic and probit regression models and one from the Adult Literacy and Life Skills (ALL) Survey for our regression model with the ordinal response variable and mismeasured covariates. / October 2016

This dissertation considers three topics under the themes of wetland restoration, urban sprawl, and recreation demand employing spatial data and analysis. A key question addressed in the first essay is how we can identify priority areas for wetlands restoration along the Louisiana coast under the Coastal Wetlands Planning, Protection, and Restoration Act by estimating amenity values received by nearby residents from hypothetical wetlands restoration projects. The second essay evaluates the effectiveness of alternative land-use policy variables for controlling development in a sprawling metropolitan area during two extreme market conditions. The third essay estimates the effect on consumer welfare from improved satisfaction of recreation information availability.

Wavelet methods possess versatile properties for statistical applications. We would like to explore the advantages of using wavelets in the analyses in two different research areas. First of all, we develop an integrated tool for online detection of network anomalies. We consider statistical change point detection algorithms, for both local changes in the variance and for jumps detection, and propose modified versions of these algorithms based on moving window techniques. We investigate performances on simulated data and on network traffic data with several superimposed attacks. All detection methods are based on wavelet packets transformations. We also propose a Bayesian model for the analysis of high-throughput data where the outcome of interest has a natural ordering. The method provides a unified approach for identifying relevant markers and predicting class memberships. This is accomplished by building a stochastic search variable selection method into an ordinal model. We apply the methodology to the analysis of proteomic studies in prostate cancer. We explore wavelet-based techniques to remove noise from the protein mass spectra. The goal is to identify protein markers associated with prostate-specific antigen (PSA) level, an ordinal diagnostic measure currently used to stratify patients into different risk groups.

The main role of roadway lighting is to produce quick, accurate and comfortable visibility during nighttime conditions. It is commonly known that good lighting levels enable motorists, pedestrians and bicyclists to obtain necessary visual information in an effective and efficient manner. Many previous studies also proved that roadway lighting minimizes the likelihood of crashes by providing better visibility for roadway users. Appropriate and adequate roadway lighting illuminance levels for each roadway classification and pedestrian areas are essential to provide safe and comfortable usage. These levels are usually provided by national, or local standards and guidelines. The Florida Department of Transportation (FDOT) Plan Preparation Manual recommends a roadway lighting illuminance level average standard of 1.0 horizontal foot candle (fc) for all the roadway segments used in this research. The FDOT Plan Preparation Manual also states that this value should be considered standard, but should be increased if necessary to maintain an acceptable uniformity illuminance ratio. This study aimed to find the relationship between nighttime crash injury severity and roadway lighting illuminance. To accomplish this, the research team analyzed crash data and roadway lighting illuminance measured in roadway segments within the West Central Florida Region. An Ordered Probit Model was developed to understand the relationship between roadway lighting illuminance levels and crash injury severity. Additionally, a Negative Binomial Model was used to determine which roadway lighting illuminance levels can be more beneficial in reducing the counts of crashes resulting in injuries. A comprehensive literature review was conducted using longitudinal studies with and without roadway lighting. Results showed that on the same roadways there was a significant decrease in the number of nighttime crashes with the presence of roadway lighting. In this research, roadway lighting illuminance was measured every 40 feet using an Advanced Lighting Measurement System (ALMS) on a total of 245 centerline miles of roadway segments within the West Central Florida Region. The data were mapped and then analyzed using the existing mile post. During the process of crash data analysis, it was observed that rear-end collisions were the most common first harmful event observed in all crashes, regardless of the lighting conditions. Meanwhile, the average injury severity for all crashes, was found to be possible injury regardless of the lighting conditions (day, dark, dusk, and dawn). Finally, this research presented an Ordered Probit Model, developed to understand the existing relationship between roadway lighting illuminance levels and injury severity within the West Central Florida Region. It was observed that having a roadway lighting average moving illuminance range between 0.4 to 0.6 foot candles (fc) was more likely to have a positive effect in reducing the probability of injury severity during a nighttime crash. A Negative Binomial Model was conducted to determine if the roadway lighting average moving illuminance level, found on the Ordered Probit Model was beneficial in reducing crash injury severity during nighttime, would also be beneficial in reducing the counts of crashes resulting in injuries. It was observed that a roadway lighting average moving illuminance, range between 0.4 to 0.6 fc, was more likely to reduce the count of crashes resulting in injuries during nighttime conditions, thus increasing roadway safety. It was also observed that other factors such as pavement condition, site location (intersection or no intersection), number of lanes, and traffic volume can affect the severity and counts of nighttime crashes. The results of this study suggest that simply adding more roadway lighting does not make the roadway safer. The fact is that a reduction in the amount of roadway lighting illuminance can produce savings in energy consumption and help the environment by reducing light pollution. Moreover, these results show that designing roadway lighting systems go beyond the initial design process, it also requires continuous maintenance. Furthermore, regulations for new developments and the introduction of additional lighting sources near roadway facilities (that are not created with the intent of being used for roadway users) need to be created.

nÃo hà / O presente trabalho busca investigar a chance de involuÃÃo financeira dentre os municÃpios cearenses, a partir dos dados contÃbeis de 150 localidades nos perÃodos de 2004, 2008 e 2012. A amostra utilizada compreende 82% do total de municÃpios no estado do Cearà e o mÃtodo utilizado segue um modelo de variÃvel dependente binÃria, com hipÃtese Probit. O modelo economÃtrico proposto considerou variÃveis de autonomia financeira, dependÃncia de transferÃncias, despesas com pessoal e encargos, gastos com educaÃÃo e gastos com saÃde. As estimativas permitem constatar que a chance à significativa de que um novo municÃpio que venha a ser criado possua arrecadaÃÃo inferior à mÃdia, sendo considerado um cenÃrio econÃmico-financeiro desfavorÃvel ao processo de emancipaÃÃo de distritos no estado do CearÃ, haja vista que os municÃpios cearenses sÃo considerados pobres e altamente dependentes de recursos de transferÃncias. / The present work search investigate the chance of financial involution among the Cearenses' municipalities, from accounting data for 150 localities in periods of 2004, 2008 and 2012. The sample comprises 82% of the total number of municipalities in the state of Cearà and the method used follows a binary dependent variable model, with Probit's hypothesis. The econometric model proposed considered variables of financial autonomy, dependence on transfers, personnel expenses and charges, education expenses and health expenses. The estimates leads us to conclude that the chance is significant in that a new municipality that will be created has fundraising less than the average, being considered a economic-financial scenario unfavorable the process of emancipation of districts in the state of CearÃ, there is a view that the Cearenses' municipalities are considered to be poor and highly dependent on features of transfers.

Our research deals with the problem of devising models for fitting non- identical dependent Bernoulli variables and using these models to predict fu- ture Bernoulli trials.We focus on modelling and predicting random Bernoulli response variables which meet all of the following conditions: 1. Each observed as well as future response corresponds to a Bernoulli trial 2. The trials are non-identical, having possibly different probabilities of occurrence 3. The trials are mutually correlated, with an underlying complex trial cluster correlation structure. Also allowing for the possible partitioning of trials within clusters into groups. Within cluster - group level correlation is reflected in the correlation structure. 4. The probability of occurrence and correlation structure for both ob- served and future trials can depend on a set of observed covariates. A number of proposed approaches meeting some of the above conditions are present in the current literature. Our research expands on existing statistical and machine learning methods. We propose three extensions to existing models that make use of the above conditions. Each proposed method brings specific advantages for dealing with correlated binary data. The proposed models allow for within cluster trial grouping to be reflected in the correlation structure. We partition sets of trials into groups either explicitly estimated or implicitly inferred. Explicit groups arise from the determination of common covariates; inferred groups arise via imposing mixture models. The main motivation of our research is in modelling and further understanding the potential of introducing binary trial group level correlations. In a number of applications, it can be beneficial to use models that allow for these types of trial groupings, both for improved predictions and better understanding of behavior of trials. The first model extension builds on the Multivariate Probit model. This model makes use of covariates and other information from former trials to determine explicit trial groupings and predict the occurrence of future trials. We call this the Explicit Groups model. The second model extension uses mixtures of univariate Probit models. This model predicts the occurrence of current trials using estimators of pa- rameters supporting mixture models for the observed trials. We call this the Inferred Groups model. Our third methods extends on a gradient descent based boosting algorithm which allows for correlation of binary outcomes called WL2Boost. We refer to our extension of this algorithm as GWL2Boost. Bernoulli trials are divided into observed and future trials; with all trials having associated known covariate information. We apply our methodology to the problem of predicting the set and total number of passengers who will not show up on commercial flights using covariate information and past passenger data. The models and algorithms are evaluated with regards to their capac- ity to predict future Bernoulli responses. We compare the models proposed against a set of competing existing models and algorithms using available air- line passenger no-show data. We show that our proposed algorithm extension GWL2Boost outperforms top existing algorithms and models that assume in- dependence of binary outcomes in various prediction metrics. / Statistics

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Food safety problems have gained national attention, and food recall is one of the most important indications of this concern. Third-party certifications have become a popular way to improve the safety and quality of products for consumers. Publications related to third-party certification usually focus on the motives and benefits of a particular certification. However, to date, no existing research investigates the effects of food recalls on certification adoption. This study uses Probit models with a binary endogenous explanatory variable to examine the relationship between food recalls and third-party certification, based on recalls occurring between January 1, 2015 and February 18, 2016. Marginal effects are used to interpret the impact of recalls and companies’ annual net sales on third-party certification adoption. Results reveal that past recalls significantly affect a firm’s likelihood of certification adoption.