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Bone cement surgery is a new technique widely used in medical field nowadays. In this thesis I analyze 48 bone cement types using their content of 20 elements. My goal is to ?find a method to classify new found bone cement sample into these 48 categories. Here I will use multinomial logistic regression method to see whether it works or not. Due to the lack of observations, I generate enough data by adding white noise in proper scales to the original data again and again, and then I get a data set of over 100 times as many points as the original one. Then I use purposeful variable selection method to pick the covariates I need, rather than stepwise selection. There are 15 covariates left after the selection, and then I use my new data set to fit such a multinomial logistic regression model. The model doesn't perform that good in goodness of ?fit test, but the result is still acceptable, and the diagnostic statistics also indicate a good performance. Combined with clinical experience and prior conditions, this model is helpful in this classification case.

Tactile sensation is a complex manifestation of mechanical stimuli applied to the skin. At the most fundamental level of the somatosensory system is the cutaneous mechanoreceptor, making it the logical starting point in the bottom-up approach to understanding the somatosensory system and sensation, in general. Unfortunately, a consensus has not been reached in terms of the afferent behavior of mechanoreceptors subjected to compressive stimulation. In this study, several afferent mechanoreceptors were isolated, mechanically stimulated with controlled compressive loads. Their responses were recorded and the sensitivities of the individual receptors to compressive stimulation were statistically evaluated by correlating the compressive state of the skin to the observed“all-or-nothing" responses. A host of linear techniques have been employed previously to describe this multiple-input, binary-output system; however, each of these techniques has associated shortcomings when employed in this context. In particular, two shortcomings are the assumption of linear system input-output and the inability of the model to assess individual input-output associations relative to concurrent input in a multivariate context with interacting input. Therefore, a non-linear regression technique called logistical regression was selected for characterizing the mechanoreceptor system. From this model, the relative contributions that each component of the stimulus has upon the neural response of the receptor can be quantitatively assessed and extrapolated to the greater population of cutaneous mechanoreceptors. Since this study represents a novel approach to receptor characterization, a framework for the application of logistical regression to the time-series representation of the multiple-input, binary-output mechanoreceptor system was established and validated. Subsequently, in-vitro experiments were performed in which the afferent behavior of tactile receptors in rat hairy skin were recorded and the relative association between a number of biologically meaningful stimulus metrics and the observed neural response was evaluated for each receptor. Through the application of logistical regression, it was determined that cutaneous mechanoreceptors are preferentially sensitive to the rate of change of compressive stress when force-control stimulated and both stress and its rate of change when position-control stimulated.

One of my previous works introduced a new data mining technique to analyze multiple experiments called TAME: Trained Across Multiple Experiments. TAME detects treatment effects of a randomized controlled experiment by utilizing data from outside of the experiment of interest. TAME with linear regression showed promising result; in all simulated scenarios, TAME was at least as good as a standard method, ANOVA, and was significantly better than ANOVA in certain scenarios. In this work, I further investigated and improved TAME by altering how TAME assembles data and creates subject models. I found that mean-centering “prior� data and treating each experiment as equally important allow TAME to detect treatment effects better. In addition, we did not find Random Forest to be compatible with TAME.

"We analyze data (length, weight and location) from a study done by the Army Corps of Engineers along the Tennessee River basin in the summer of 1980. The purpose is to predict the probability that a hypothetical channel catfish at a location studied is toxic and contains 5 ppm or more DDT in its filet. We incorporate spatial information and treate it separetely from other covariates. Ultimately, we want to predict the probability that a catfish from the unobserved location is toxic. In a preliminary analysis, we examine the data for observed locations using frequentist logistic regression, Bayesian logistic regression, and Bayesian logistic regression with random effects. Later we develop a parsimonious extension of Bayesian logistic regression and the corresponding Gibbs sampler for that model to increase computational feasibility and reduce model parameters. Furthermore, we develop a Bayesian model to impute data for locations where catfish were not observed. A comparison is made between results obtained fitting the model to only observed data and data with missing values imputed. Lastly, a complete model is presented which imputes data for missing locations and calculates the probability that a catfish from the unobserved location is toxic at once. We conclude that length and weight of the fish have negligible effect on toxicity. Toxicity of these catfish are mostly explained by location and spatial effects. In particular, the probability that a catfish is toxic decreases as one moves further downstream from the source of pollution."

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This thesis deals with estimation and inference in two semiparametric problems: a two-component mixture model and a single index regression model. For the two-component mixture model, we assume that the distribution of one component is known and develop methods for estimating the mixing proportion and the unknown distribution using ideas from shape restricted function estimation. We establish the consistency of our estimators. We find the rate of convergence and the asymptotic limit of our estimator for the mixing proportion. Furthermore, we develop a completely automated distribution-free honest finite sample lower confidence bound for the mixing proportion. We compare the proposed estimators, which are easily implementable, with some of the existing procedures through simulation studies and analyse two data sets, one arising from an application in astronomy and the other from a microarray experiment. For the single index model, we consider estimation of the unknown link function and the finite dimensional index parameter. We study the problem when the true link function is assumed to be: (1) smooth or (2) convex. When the link function is just assumed to be smooth, in contrast to standard kernel based methods, we use smoothing splines to estimate the link function. We prove the consistency and find the rates of convergence of the proposed estimators. We establish root-n-rate of convergence and the semiparametric efficiency of the parametric component under mild assumptions. When the link function is assumed to be convex, we propose a shape constrained penalized least squares estimator and a Lipschitz constrained least squares estimator for the unknown quantities. We prove the consistency and find the rates of convergence for both estimators. For the shape constrained penalized least squares estimator, we establish root-n-rate of convergence and the semiparametric efficiency of the parametric component under mild assumptions and conjecture that the parametric component of the Lipschitz constrained least squares estimator is semiparametrically efficient. We develop the R package "simest'' that can be used (to compute the proposed estimators) even for moderately large dimensions.

This thesis includes three substantive empirical studies (in Chapters 3, 4 and 5), where each study uses the same econometric methodology, named Regression Discontinuity design, which has an attractive feature - local randomisation. This feature has given the superiority of the method over the other evaluation methods in estimating unbiased treatment effects. Besides, the fuzzy Regression Discontinuity design can control for the endogeneity of the treatment variable, which is another advantage of the method. In each of the studies considered, the endogeneity problem exists. The application of the fuzzy Regression Discontinuity design is itself a contribution in each of the studies. Moreover, each study contributes in its own field. In Chapter 3, we investigate how much the Social Safety Net programs, that provide free food, or cash, or both to the food insecure households in Bangladesh, improve calorie consumption of the beneficiary households. Using Household Income and Expenditure Survey 2005, we find that the effect of the programs is around 843 kilo calorie, which is substantial compared to the previous studies. In Chapter 4, we examine how much was the impact of Education Maintenance Allowance, a program that provided weekly allowance to the young people in Years 12 and 13 in England, on the staying rate in the post compulsory full-time education. The program was abolished in 2010. Using the Longitudinal Survey of Young People in England, we find that the effect of the program was substantial - around 15 percent. The effect of a £1 increase in weekly allowance was around 1 percent. These effects were mainly on the white young people. Using the household survey data - Family Expenditure Survey (1968-2009) - in UK, Chapter 5 establishes that before 1981 consumption substantially fell at the retirement age. This fall is less severe after 1980. However, throughout the data period, consumption fall at the retirement age is fully explained by the expected fall in income, which contradicts the life cycle model, where a consumption growth is independent of an income growth.

In general model selection so far considered in literature, the parameter estimation loss and the prediction loss from the model selected are considered to be the same. In this thesis, the methods of parameter estimation may vary with different estimation loss, and the model selection may be based on different prediction loss. Under some regularized conditions, a model selection criterion, called generalized risk criterion (GRC), is proposed with a closed form. For multivariate linear regression model, and Cox regression model for ranking data, our studies that this criterion is an extension of the model selection criterion AIC. We also demonstrate that GRC performs better than AIC in a practical semi-parametric regression problem involving investments on horse racing. / Keywords: Variable selection; Model selection criterion; AIC; GRC; Loss function; Risk function; Multinomial Choice Model; Cox model for ranking data. / Searching for the true model based on the limited data is usually an impossible task. More and more attention in research has been focused on how to find an optimal model based on some special objective, such as focused information criterion (FIC, Hjort and Claeskens, 2003 [15]), Subspace Information criterion (Sugiyama and Ogawa, 2001 [43]) in statistical learning, etc. These ideas also motivate us to find an optimal subset of variables based on some objective. Different objectives may result in different choices of subset of variables. / Variable selection, an important aspect of model selection, is applied widely in real practices to explore the latent relationship between the random phenomena and various factors. Many model selection criteria, such as Mallow's Cp (Mallows, 1964 [28]). PRESS (Allen, 1971 [3]). AIC (Akaike, 1973 [2]), are proposed for seeking the optimal subset of the variables. Most of them try to find a criterion based on the observed data such that the selected models perform well both for fitting and for prediction. / Zuo, Guo Xin. / "July 2007." / Adviser: Ming Gao Gu. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0402. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 71-75) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

by Ka-Kit Tse. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references. / Acknowledgments --- p.i / List of tables --- p.v / Chapter Chapter 1: --- Overall Review --- p.1 / Chapter Chapter 2: --- Essay one - A Mathematical Programming Approach to Clusterwise Regression Model and its Extensions / Chapter 2.0. --- Abstract --- p.5 / Chapter 2.1. --- Introduction --- p.6 / Chapter 2.2. --- A Mathematical Programming Formulation of the Clusterwise Regression Model --- p.10 / Chapter 2.2.1. --- The Generalized Clusterwise Regression Model --- p.10 / Chapter 2.2.2. --- "Clusterwise Regression Model (Spath, 1979)" --- p.14 / Chapter 2.2.3. --- A Nonparametric Clusterwise Regression Model --- p.15 / Chapter 2.2.4. --- A Mixture Approach to Clusterwise Regression Model --- p.16 / Chapter 2.2.5. --- An Illustrative Application --- p.19 / Chapter 2.3. --- Mathematical Programming Formulation of the Clusterwise Discriminant Analysis --- p.21 / Chapter 2.4. --- Conclusion --- p.25 / Chapter 2.5. --- Appendix --- p.28 / Chapter 2.6. --- References --- p.32 / Chapter 2.7. --- Tables --- p.35 / Chapter Chapter 3: --- Essay two - A Mathematical Programming Approach to Clusterwise Rank Order Logit Model / Chapter 3.0. --- Abstract --- p.40 / Chapter 3.1. --- Introduction --- p.41 / Chapter 3.2. --- Clusterwise Rank Order Logit Model --- p.42 / Chapter 3.3. --- Numerical Illustration --- p.46 / Chapter 3.4. --- Conclustion --- p.48 / Chapter 3.5. --- References --- p.50 / Chapter 3.6. --- Tables --- p.52 / Chapter Chapter 4: --- Essay three - A Mathematical Programming Approach to Metric Unidimensional Scaling / Chapter 4.0. --- Abstract --- p.53 / Chapter 4.1. --- Introduction --- p.54 / Chapter 4.2. --- Nonlinear Programming Formulation --- p.56 / Chapter 4.3. --- Numerical Examples --- p.60 / Chapter 4.4. --- Possible Extensions --- p.61 / Chapter 4.5. --- Conclusion and Extensions --- p.63 / Chapter 4.6. --- References --- p.64 / Chapter 4.7. --- Tables --- p.66 / Chapter Chapter 5: --- Research Project in Progress / Chapter 5.1. --- Project 1 -- An Integrated Approach to Taste Test Experiment Within the Prospect Theory Framework --- p.68 / Chapter 5.1.1. --- Experiment Procedure --- p.68 / Chapter 5.1.2. --- Experimental Result --- p.72 / Chapter 5.2. --- Project 2 -- An Integrated Approach to Multi- Dimensional Scaling Problem --- p.75 / Chapter 5.2.1. --- Introduction --- p.75 / Chapter 5.2.2. --- Experiment Procedure --- p.76 / Chapter 5.2.3. --- Questionnaire --- p.78 / Chapter 5.2.4. --- Experimental Result --- p.78