High levels of automation in manufacturing industries are leading to data sets of increasing size and dimension. The challenge facing statisticians and field professionals is to develop methodology to help meet this demand. Functional data is one example of high-dimensional data characterized by observations recorded as a function of some continuous measure, such as time. An application considered in this thesis comes from the automotive industry. It involves a production process in which valve seats are force-fitted by a ram into cylinder heads of automobile engines. For each insertion, the force exerted by the ram is automatically recorded every fraction of a second for about two and a half seconds, generating a force profile. We can think of these profiles as individual functions of time summarized into collections of curves. The focus of this thesis is the analysis of functional process data such as the valve seat insertion example. A number of techniques are set forth. In the first part, two ways to model a single curve are considered: a b-spline fit via linear regression, and a nonlinear model based on differential equations. Each of these approaches is incorporated into a mixed effects model for multiple curves, and multivariate process monitoring techniques are applied to the predicted random effects in order to identify anomalous curves. In the second part, a Bayesian hierarchical model is used to cluster low-dimensional summaries of the curves into meaningful groups. The belief is that the clusters correspond to distinct types of processes (e.g. various types of “good” or “faulty” assembly). New observations can be assigned to one of these by calculating the probabilities of belonging to each cluster. Mahalanobis distances are used to identify new observations not belonging to any of the existing clusters. Synthetic and real data are used to validate the results.

This dissertation describes a minimum distance method for density estimation when the variable of interest is not directly observed. It is assumed that the underlying target density can be well approximated by a mixture of normals. The method compares a density estimate of observable data with a density of the observable data induced from assuming the target density can be written as a mixture of normals. The goal is to choose the parameters in the normal mixture that minimize the distance between the density estimate of the observable data and the induced density from the model. The method is applied to the deconvolution problem to estimate the density of $X_{i}$ when the variable $% Y_{i}=X_{i}+Z_{i}$, $i=1,\ldots ,n$, is observed, and the density of $Z_{i}$ is known. Additionally, it is applied to a location random effects model to estimate the density of $Z_{ij}$ when the observable quantities are $p$ data sets of size $n$ given by $X_{ij}=\alpha _{i}+\gamma Z_{ij},~i=1,\ldots ,p,~j=1,\ldots ,n$, where the densities of $\alpha_{i} $ and $Z_{ij}$ are both unknown. The performance of the minimum distance approach in the measurement error model is compared with the deconvoluting kernel density estimator of Stefanski and Carroll (1990). In the location random effects model, the minimum distance estimator is compared with the explicit characteristic function inversion method from Hall and Yao (2003). In both models, the methods are compared using simulated and real data sets. In the simulations, performance is evaluated using an integrated squared error criterion. Results indicate that the minimum distance methodology is comparable to the deconvoluting kernel density estimator and outperforms the explicit characteristic function inversion method.

Many studies suggest the ability of the NAIC Risk-Based Capital ratio (RBC ratio) to predict insurer insolvency. Based on the US life insurer (insurer) data for the period of 2005 to 2008, this study finds explanatory variables that have a statistically significant relationship with the RBC ratio. Advantages of panel data over cross-sectional and time series data analysis are exploited to make valid inference on coefficients of the explanatory variables. Testing for unobserved insurer and time effects and for dependence between these effects and the explanatory variables indicates the appropriateness of the fixed insurer and time effects model. Based on the ordinary least squares estimates, it is found that insurers' size, capital-to-asset ratio, and return on capital have a statistically significant relationship with the RBC ratio. Additionally, health product, annuity product, opportunity, and regulatory risks of insurers are related to the RBC ratio. Accounting for heteroscedasticity and autocorrelation for a given insurer yields the same coefficient estimates, but increased standard errors. / text

We considered a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows to choose a simple, conditionally conjugate normal prior on the Cholesky factor. Based on the non-centered parameterization, we search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors using Bayesian variable selection methods. With this method we are able to learn from the data for each effect, whether it is random or not, and whether covariances among random effects are zero or not. An application in marketing shows a substantial reduction of the number of free elements of the variance-covariance matrix. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

This dissertation addresses issues that arise in the classic linear instrumental variables (IV) model when some of the underlying assumptions are violated. / Economics

Vitamin K has a negligible effect on bone mineral density (BMD) and a large but uncertain effect on fractures. The three studies in the thesis explored uncertainty about the effect of vitamin K on fractures using the methods of economic evaluation and Bayesian meta-analysis. In study 1, a Markov probabilistic microsimulation model was developed for a hypothetical cohort of 50-year-old postmenopausal women without osteoporosis. This was a fracture incidence-based model, populated with data from the literature. It was used to examine the cost-effectiveness of two supplementation strategies over a lifetime horizon. We compared vitamin K2 (or vitamin K1) concurrent with vitamin D3 and calcium versus vitamin D3 and calcium alone. Study 2 included a systematic review, and classical and Bayesian univariate meta-analyses to determine the efficacies of the K vitamins on BMD or fractures in current and future trials. Study 3 used Bayesian bivariate random-effects meta-analysis to jointly model the treatment effects on two correlated bone outcomes. We compared the estimates from the univariate and bivariate meta-analyses and explored how these results would change the conclusions of the cost-effectiveness analysis. The strategies including vitamin K were highly cost-effective at willingness-to-pay of $50,000/QALY (quality-adjusted life year); however, the results were most sensitive to changes in the efficacy of vitamin K. The univariate meta-analyses showed large uncertainties in the anti-fracture effects of vitamin K2 in current and future trials. The bivariate 95% credible intervals were considerably narrower than those from the univariate meta-analyses. Using future odds ratios from the bivariate meta-analyses, vitamin K2 cost more than $100,000/QALY while vitamin K1 was cost-saving. Our analyses found substantial uncertainty around the estimates of the vitamin K effect on fractures. We recommend against routine use of vitamin K for fracture prevention. Bayesian bivariate meta-analysis accounts for all available information and should be considered when the treatment effects are measured on two correlated outcomes.

Vitamin K has a negligible effect on bone mineral density (BMD) and a large but uncertain effect on fractures. The three studies in the thesis explored uncertainty about the effect of vitamin K on fractures using the methods of economic evaluation and Bayesian meta-analysis. In study 1, a Markov probabilistic microsimulation model was developed for a hypothetical cohort of 50-year-old postmenopausal women without osteoporosis. This was a fracture incidence-based model, populated with data from the literature. It was used to examine the cost-effectiveness of two supplementation strategies over a lifetime horizon. We compared vitamin K2 (or vitamin K1) concurrent with vitamin D3 and calcium versus vitamin D3 and calcium alone. Study 2 included a systematic review, and classical and Bayesian univariate meta-analyses to determine the efficacies of the K vitamins on BMD or fractures in current and future trials. Study 3 used Bayesian bivariate random-effects meta-analysis to jointly model the treatment effects on two correlated bone outcomes. We compared the estimates from the univariate and bivariate meta-analyses and explored how these results would change the conclusions of the cost-effectiveness analysis. The strategies including vitamin K were highly cost-effective at willingness-to-pay of $50,000/QALY (quality-adjusted life year); however, the results were most sensitive to changes in the efficacy of vitamin K. The univariate meta-analyses showed large uncertainties in the anti-fracture effects of vitamin K2 in current and future trials. The bivariate 95% credible intervals were considerably narrower than those from the univariate meta-analyses. Using future odds ratios from the bivariate meta-analyses, vitamin K2 cost more than $100,000/QALY while vitamin K1 was cost-saving. Our analyses found substantial uncertainty around the estimates of the vitamin K effect on fractures. We recommend against routine use of vitamin K for fracture prevention. Bayesian bivariate meta-analysis accounts for all available information and should be considered when the treatment effects are measured on two correlated outcomes.

This thesis investigates why and how macroeconomic volatility in source countries interacts with their FDI outflows. The study focuses on FDI flowing out from OECD countries to less developed countries in the ASEAN region. Using a panel data encompassing 52 country-pairs over the period 1996-2011, I find a negative correlation between FDI outflows and macroeconomic volatility in source countries. More specifically the empirical results suggest an adverse relationship between inflation and output volatility (business cycles fluctuations) and FDI flows – the more macroeconomic volatility in developed economies the lesser FDI flows to less developed economies, which is explained by Keynesian theories. These findings derive from a gravity model approach, which enabled me to control for host country determinants. In order to estimate these relationships I adopted a random effects model and a tobit model. The reason behind the use of these two models derives from the different views within this branch of research because of censored FDI statistics. The thesis is inspired by Éric Rougier’s et al. work on how macroeconomic volatility in European countries interacts with FDI flows to the MENA region (2012).

Longitudinal studies, where data on study subjects are collected over time, is increasingly involving multivariate longitudinal responses. Frequently, the heterogeneity observed in a multivariate longitudinal response can be attributed to underlying unobserved disease states in addition to any between-subject differences. We propose modeling such disease states using a hidden Markov model (HMM) approach and expand upon previous work, which incorporated random effects into HMMs for the analysis of univariate longitudinal data, to the setting of a multivariate longitudinal response. Multivariate longitudinal data are modeled jointly using separate but correlated random effects between longitudinal responses of mixed data types in addition to a shared underlying hidden process. We use a computationally efficient Bayesian approach via Markov chain Monte Carlo (MCMC) to fit such models. We apply this methodology to bivariate longitudinal response data from a smoking cessation clinical trial. Under these models, we examine how to incorporate a treatment effect on the disease states, as well as develop methods to classify observations by disease state and to attempt to understand patient dropout. Simulation studies were performed to evaluate the properties of such models and their applications under a variety of realistic situations.

abstract: Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex represents the location of the curve in the XY plane. For a quadratic growth curve, we propose an approximate confidence region as well as the confidence interval for x and y-coordinates of the vertex using two methods, the gradient method and the delta method. Under some models, an indirect test on the location of the curve can be based on the intercept and slope parameters, but in other models, a direct test on the vertex is required. We present a quadratic-form statistic for a test of the null hypothesis that there is no shift in the location of the vertex in a linear mixed model. The statistic has an asymptotic chi-squared distribution. For 2nd degree polynomials of two independent samples, we present an approximate confidence region for the difference of vertices of two quadratic growth curves using the modified gradient method and delta method. Another chi-square test statistic is derived for a direct test on the vertex and is compared to an F test statistic for the indirect test. Power functions are derived for both the indirect F test and the direct chi-square test. We calculate the theoretical power and present a simulation study to investigate the power of the tests. We also present a simulation study to assess the influence of sample size, measurement occasions and nature of the random effects. The test statistics will be applied to the Tell Efficacy longitudinal study, in which sound identification scores and language protocol scores for children are modeled as quadratic growth curves for two independent groups, TELL and control curriculum. The interpretation of shift in the location of the vertices is also presented. / Dissertation/Thesis / Doctoral Dissertation Statistics 2015