Traffic fatalities accounted for 1.24 million lives lost in 2013 worldwide, and almost 33 thousand of those fatalities were in the U.S. in 2013. The southeastern region of the nation stands out for continuously having higher fatality rates per mile driven than the national average. If one can establish compelling relationships between various factors and fatality rates, then policies and investments can be targeted to increase the safety on the network by focusing on policies that mitigate those factors. In this research effort risk-taking characteristics are explored. These factors have not been as comprehensively reviewed as conventional factors such as vehicle and facility conditions associated with safety. The hypothesis assumes if a person exhibits risk-taking behavior, that risk-taking behavior is not limited to only one aspect of risk, but is likely to occur in multiple facets of the person's life. Some of the risk-taking characteristics explored include credit score, safety belt use, smoking and tobacco use, drug use, mental health, educational attainment, obesity, and overall general health characteristics. All risk-taking characteristics with the exception of mental health were found to have statistically significant correlations with fatality rates alone. However, when a regression model was formed to estimate fatality rates by risk-taking characteristics, only four risk-taking characteristics - credit score, educational attainment, overall poor health, and seat belt use were found to be statistically significant at an integrated level with other demographic characteristics such as unemployment levels and population born is state of residency. By identifying at-risk population segments, education, counseling, enforcement, or other strategies may be deployed to help improve travel safety.

自1980年代後期Hull & White、Wiggins、Johnson & Shanno等人相繼發表關於隨機波動度模型的文獻後，就有諸多的文獻對於在選擇權定價中考慮隨機波動度作更深入的分析與模型探討，然而關於隨機波動度的研究，在早期大多採用蒙地卡羅模擬法來分析選擇權的價格行為，但蒙地卡羅模擬法受限於運算效率不高與缺乏彈性，故在評價新奇選擇權，如美式選擇權、障礙選擇權時，並無法應用。故本文以Leisen（2000）的二元樹狀模型出發，探討在不同相關係數及參數設定下之各類選擇權的定價、避險參數及隱含波動度曲面模擬計算等主題。 最後我們得到下面幾點結論： 1.在收斂速度與運算效率方面，我們可以發現二元樹狀模型在分割期數n大於20時，計算價格與收斂價格的差距就非常微小，而若我們計算不同切割期數的最大價格差異也會發現其實都不到百分之一，因此整體而言，收斂速度是令人非常滿意的。 2.當期初波動度提高時，會縮小價外選擇權與B-S價格之間的價格誤差。當到期期限增加時，隱含波動度曲線會有整體提高的趨勢。 3.若提高波動係數σ為2.5時，則不論相關係數的正負情形，價內外的程度，皆會大幅提高選擇權的隱含波動度。而在相關係數為-0.5的時候，可以發現實證中常觀察到的隱含波動度微笑曲線，這可能代表著市場上的波動係數比我們預期中的都還來的高。 4.在進行不同相關係數及不同價內外程度下二元樹狀與單元樹狀模型的美式選擇權價格比較時，我們可以發現，若以二元樹狀模型為正確價格，當相關係數為負的時候，在價外的時候，單元樹狀模型有價格低估的現象，在價內的時候，則有價格高估的現象，而在相關係數為正的時候，則反之。 5.Leisen二元樹狀與封閉解的歐式向上出局賣權價格比較，在特定的參數設定之下，Leisen二元樹狀模型在評價歐式向上出局賣權的時候，當相關係數為負的時候，在價外的時候，模型價格會高於封閉解，在價內的時候，模型價格則會低於封閉解，而在相關係數為正的時候，則反之。

Bivariate or multivariate correlated data may be collected on a sample of unit in many applications. When the experimenters concern about the failure times of two related subjects for example paired organs or two chronic diseases, the bivariate binary data is often acquired. This type of data consists of a observation point x and indicators which represent whether the failure times happened before or after the observation point. In this work, the observed bivariate data can be written with the following form {x, £_1=I(X1≤ x), £_2=I(X2≤ x)}.The corresponding optimal design problems for parameter estimation under this type of bivariate data are discussed. For this kind of the multivariate responses with explanatory variables, their marginal distributions may be from different distributions. Copula model is a way to formulate the relationship of these responses, and the association between pairs of responses. Copula models for bivariate binary data are considered useful in practice due to its flexibility. In this dissertation for bivariate binary data, the marginal functions are assumed from exponential or Weibull distributions and two assumptions, independent or correlated, about the joint function between variables are considered. When the bivariate binary data is assumed correlated, the Clayton copula model is used as the joint cumulative distribution function. There are few works addressed the optimal design problems for bivariate binary data with copula models. The D-optimal designs aim at minimizing the volume of the confidence ellipsoid for estimating unknown parameters including the association parameter in bivariate copula models. They are used to determine the best observation points. Moreover, the Ds-optimal designs are mainly used for estimation of the important association parameter in Clayton model. The D- and Ds-optimal designs for the above copula model are found through the general equivalence theorem with numerical algorithm. Under different model assumptions, it is observed that the number of support points for D-optimal designs is at most as the number of model parameters for the numerical results. When the difference between the marginal distributions and the association are significant, the association becomes an influential factor which makes the number of supports gets larger. The performances of estimation based on optimal designs are reasonably well by simulation studies. In survival experiments, the experimenter customarily takes trials at some specific points such as the position of the 25, 50 and 75 percentile of distributions. Hence, we consider the design efficiencies when the design points for trials are at three or four particular percentiles. Although it is common in practice to take trials at several quantile positions, the allocations of the proportion of sample size also have great influence on the experimental results. To use a locally optimal design in practice, the prior information for models or parameters are needed. In case there is not enough prior knowledge about the models or parameters, it would be more flexible to use sequential experiments to obtain information in several stages. Hence with robustness consideration, a sequential procedure is proposed by combining D- and Ds-optimal designs under independent or correlated distribution in different stages of the experiment. The simulation results based on the sequential procedure are compared with those by the one step procedures. When the optimal designs obtained from an incorrect prior parameter values or distributions, those results may have poor efficiencies. The sample mean of estimators and corresponding optimal designs obtained from sequential procedure are close to the true values and the corresponding efficiencies are close to 1. Huster (1989) analyzed the corresponding modeling problems for the paired survival data and applied to the Diabetic Retinopathy Study. Huster (1989) considered the exponential and Weibull distributions as possible marginal distributions and the Clayton model as the joint function for the Diabetic Retinopathy data. This data was conducted by the National Eye Institute to assess the effectiveness of laser photocoagulation in delaying the onset of blindness in patients with diabetic retinopathy. This study can be viewed as a prior experiment and provide the experimenter some useful guidelines for collecting data in future studies. As an application with Diabetic Retinopathy Study, we develop optimal designs to collect suitable data and information for estimating the unknown model parameters. In the second part of this work, the optimal design problems for parameter estimations are considered for the type of proportional data. The nonlinear model, based on Jorgensen (1997) and named the dispersion model, provides a flexible class of non-normal distributions and is considered in this research. It can be applied in binary or count responses, as well as proportional outcomes. For continuous proportional data where responses are confined within the interval (0,1), the simplex dispersion model is considered here. D-optimal designs obtained through the corresponding equivalence theorem and the numerical results are presented. In the development of classical optimal design theory, weighted polynomial regression models with variance functions which depend on the explanatory variable have played an important role. The problem of constructing locally D-optimal designs for simplex dispersion model can be viewed as a weighted polynomial regression model with specific variance function. Due to the complex form of the weight function in the information matrix is considered as a rational function, an approximation of the weight function and the corresponding optimal designs are obtained with different parameters. These optimal designs are compared with those using the original weight function.

When using data for estimating the parameters in a bivariate distribution, the tradition is to assume that data comes from a bivariate normal distribution. If the distribution is not bivariate normal, which often is the case, the maximum likelihood (ML) estimators are intractable and the least square (LS) estimators are inefficient. Here, we consider two independent sets of bivariate data which come from non-normal populations. We consider two distinctive distributions: the marginal and the conditional distributions are both Generalized Logistic, and the marginal and conditional distributions both belong to the Student&rsquo / s t family. We use the method of modified maximum likelihood (MML) to find estimators of various parameters in each distribution. We perform a simulation study to show that our estimators are more efficient and robust than the LS estimators even for small sample sizes. We develop hypothesis testing procedures using the LS and the MML estimators. We show that the latter are more powerful and robust. Moreover, we give a comparison of our tests with another well known robust test due to Tiku and Singh (1982) and show that our test is more powerful. The latter is based on censored normal samples and is quite prominent (Lehmann, 1986). We also use our MML estimators to find a more efficient estimator of Mahalanobis distance. We give real life examples.

In this thesis, a simulation study is held and a statistical model is fitted to the simulated data. This data is assumed to be the satisfaction of the customers who withdraw their salary from a particular bank. It is a longitudinal data which has bivariate and binary response. It is assumed to be collected from 200 individuals at four different time points. In such data sets, two types of dependence -the dependence within subject measurements and the dependence between responses- are important and these are considered in the model. The model is Marginalized Transition Random Effects Models, which has three levels. The first level measures the effect of covariates on responses, the second level accounts for temporal changes, and the third level measures the difference between individuals. Markov Chain Monte Carlo methods are used for the model fit. In the simulation study, the changes between the estimated values and true parameters are searched under two conditions, when the model is correctly specified or not. Results suggest that the better convergence is obtained with the full model. The third level which observes the individual changes is more sensitive to the model misspecification than the other levels of the model.

Six new structural parameters £rB, £pB, £rC, £pC, £rS, and £pS are proposed to enhance the side chain actions in protein structures. Programs for calculating these new parameters based on phi and psi torsion angles vector algebra calculation method are established. A bivariate model with von Mises marginal distributions are applied to establish models of phi and psi in protein class Ophiophagus hannah neurotoxins and alpha-bungarotoxins respectively. 11 global structural parameters include phi and psi torsion angles, bond lengths of C-N, C-O, C£\ -C, and N-C£\, and bond angles of C-N-C£\, C£\-C-N, C£\-C-O, N-C£\-C, and O-C-N are considered to classify long alpha-neurotoxins by Ward's cluster method and LIBSVM program package. Those global structural parameters of loop II Trp residues of alpha-neurotoxins are discussed.

The method of least squares has been used in general for regression analysis. It is usually assumed that the errors are confined to the dependent variable, but in many cases both dependent and independent variables are typically measured with some stochastic errors. The statistical method of orthogonal regression has been used when both variables under investigation are subject to stochastic errors. Furthermore, the measurements sometimes may not be exact but have been censored. In this situation doing orthogonal regression with censored data directly between the two variables, it may yield an incorrect estimates of the relationship. In this work we discuss the estimation of orthogonal regression under censored data in one variable and then provide a method of estimation and two criteria on when the method is applicable. When the observations satisfy the criteria provided here, there will not be very large differences between the estimated orthogonal regression line and the theoretical orthogonal regression line.

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We examine the gender gap in school attendance of children aged 7-14 in India using National Family Health Survey Three (NFHS-3). We demonstrate that the choice of the sample examined has important implications for policy. A household decision model is used to motivate whether a child attends school and/or works. A bivariate probit model and Blinder-Oaxaca Decomposition are applied to see how changing sample groups and adding regressors impact results, and the implications this has upon gender gap and effectiveness of centralized policy as opposed to decentralized policy. Results show the gender gap is sensitive to the sub samples chosen (e.g. a particular state, a specific location (urban or rural), and gender) and to the choice of regressors, and that centralized policy may be less effective than decentralized policy. Parental education, wealth, location and gender are found to be the most volatile and influential variables in the household decision process. / Graduate

Research Doctorate - Doctor of Philosophy (PhD) / Due to the effects of global warming and climate change there is currently intense and growing international interest in suitable modelling methods for relating satellite remotely sensed spectral imagery of vegetated landscapes to the biophysical structural variables in those landscapes across regional, continental or global scales. Of particular interest here is the satellite optical remote sensing of forest foliage cover—measured as foliage projective cover (FPC)—by Landsat ETM+ (Enhanced Thematic Mapper plus) sensor. In the remote sensing literature, different empirical and physical modelling approaches exist for relating remotely sensed imagery to the landscape parameters of interest, each with their own advantages and disadvantages. These approaches, in the main, may be broadly categorised as belonging to one, or a combination of: spectral mixture analysis (SMA) modelling, canopy reflectance modelling, multiple regression (MR) modelling or, spectral vegetation index (SVI) modelling. This thesis uses the SVI approach, partly in comparison to the MR approach. Both the SVI and MR approaches require field-based data to establish the relationship between the biophysical parameter and the spectral index or spectral responses within defined spectral bandwidths. Surrogate measures of the biophysical parameter are sometimes used extensively to establish this relationship and therefore a separate calibration relationship is required.This has inherent problems when the output of one model is substituted into the next and the effects of carry-over of error from one model to the next are not considered. My main goal is therefore to develop a modelling approach that will allow a larger set of one or more surrogate measures to be combined with a smaller set of ‘true’ measures of the biophysical parameter into the one model for establishing the relationship with the SVI and hence the spectral imagery. Success in meeting the goal is the illustration of a working model using real data. In progression towards meeting the goal, two new modelling ideas are developed and synthesised into the creation of an overall modelling framework for estimating FPC from spectral imagery. The modelling framework, which has potential for use in other applications, allows for the incorporation of different types of data including different calibration relationships between variables while avoiding the usual, stepwise approach to the linking of separate relationship models and their variables. One contribution that is new to both remote sensing and statistical modelling practices involves a polar transformation of the principal components of a multi-spectral image of a local reference landscape to produce a set of empirically based, invariant three-dimensional spectral index transformations that have potential for application to the spectral images of different regional landscapes and possibly global landscapes. In particular, the vegetation index from the set has approximate bounded properties that we exploit for modelling of its contribution to residual variation in its relationships with the biophysical variables measured on the ground. The other contribution to statistical modelling practice that has potential for application by a wide range of disciplines is the direct modelling of interdependent relationships between pairs of bounded variates, each considered to have a measurement error structure that can be modelled as though it is similar to sampling variation. Associated with this particular contribution is the development of novel geometric methods to construct approximate prediction bounds and to assist with model interpretations.