Latent variables are often included in a model in order to capture the diversity among subjects in a population. Sometimes the distribution of these latent variables are of principle interest. In studies where sequences of observations are taken from subjects, ancillary variables, such as the number of observations provided by each subject, usually also vary between subjects. The goal here is to understand efficient estimation of the expectation of the latent variable in the presence of these subject-specific ancillaries. Unbiased estimation and efficient estimation of the expectation of the latent parameter depend on the dependence structure of these three subject-specific components: latent variable, sequence of observations, and ancillary. This dissertation considers estimation under two dependence configurations. In Chapter 3, efficiency is studied under the model in which no assumptions are made about the joint distribution of the latent variable and the subject-specific ancillary. Chapter 4 treats the setting where the ancillary variable and the latent variable are independent.

Yim Tsz-ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 47-49). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Local Polynomial Modeling --- p.4 / Chapter 2.1 --- Local Polynomial Fitting --- p.4 / Chapter 2.1.1 --- Methodology --- p.4 / Chapter 2.1.2 --- The kernel K --- p.6 / Chapter 2.1.3 --- The bandwidth h --- p.7 / Chapter 2.1.4 --- The order p --- p.10 / Chapter 2.2 --- Estimation of Conditional Density --- p.11 / Chapter 3 --- Bandwidth Selection --- p.14 / Chapter 3.1 --- Rule of Thumb --- p.14 / Chapter 3.2 --- Bootstrap Bandwidth Selection --- p.15 / Chapter 3.3 --- A Cross-Validation Method --- p.16 / Chapter 4 --- A Theoretical Justification --- p.18 / Chapter 4.1 --- Proof of (4.1) --- p.19 / Chapter 4.2 --- Proof of (4.2) --- p.22 / Chapter 5 --- Simulation Studies --- p.25 / Chapter 6 --- Real Data Applications --- p.38 / Chapter 6.1 --- Case Study With Canadian Lynx Data.............................. --- p.38 / Chapter 6.2 --- Case Study With U.S. Twelve-Month Treasury Bill Data.......... --- p.41 / Chapter 7 --- Conclusions --- p.45 / Bibliography --- p.47

Hung, King Chi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 78-52). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Non-linear Time Series Models and Their Applications --- p.2 / Chapter 1.2 --- The SETAR Model --- p.4 / Chapter 1.3 --- Objectives and Organization of the Thesis --- p.6 / Chapter 2 --- The SETAR Model and Robust Test for Non-linearity --- p.8 / Chapter 2.1 --- A Brief Review of Existing Tests for Threshold-type Non-linearity --- p.9 / Chapter 2.2 --- Robust Tests for Threshold-type Non-linearity --- p.11 / Chapter 2.2.1 --- Tsay´ةs F Test --- p.12 / Chapter 2.2.2 --- The Proposed Test --- p.15 / Chapter 2.3 --- The Choice of the ψ-function --- p.23 / Chapter 2.4 --- A Simulation Study --- p.26 / Chapter 2.4.1 --- Data Generation Process (DGP) --- p.26 / Chapter 2.4.2 --- Simulation Findings --- p.29 / Chapter 3 --- Robust Estimation and Asymptotic Properties --- p.34 / Chapter 3.1 --- Least Squares Estimation --- p.37 / Chapter 3.2 --- Robust Estimation --- p.38 / Chapter 3.2.1 --- Asymptotic Properties --- p.40 / Chapter 3.3 --- A Simulation Study --- p.52 / Chapter 3.3.1 --- Data Generation Process (DGP) --- p.53 / Chapter 3.3.2 --- Simulation Findings --- p.55 / Chapter 3.3.3 --- Objective Function over r --- p.56 / Chapter 4 --- Numerical Example --- p.67 / Chapter 4.1 --- Methodology --- p.68 / Chapter 4.2 --- ASEAN Background --- p.69 / Chapter 4.2.1 --- Non-linearity tests on ASEAN Exchange Rate --- p.72 / Chapter 4.2.2 --- Estimation of the Return of Singaporean Dollar --- p.73 / Chapter 5 --- Conclusions and Further Research --- p.76 / References --- p.78

This thesis investigates whether estimating the inputs of the Markowitz (1952) Mean- Variance framework using various econometric techniques leads to improved optimal portfolio allocations at the country, sector and stock levels over a number of time periods. We build upon previous work by using various combinations of conventional and Bayesian expected returns and covariance matrix estimators in a Mean-Variance framework that incorporates a benchmark reference, an allowable deviation range from the benchmark weights and short-selling constraints so as to achieve meaningful and realistic outcomes. We found that models based on the classical maximum likelihood method performed just as well as the more sophisticated Bayesian return estimators in the study. We also found that the covariance matrix estimators analysed created covariance matrices that were similar to one another and, as a result, did not seem to have a large effect on the overall portfolio allocation. A sensitivity analysis on the level of risk aversion confirmed that the simulation results were robust for the different levels of risk aversion.

Telecommunication networks become major parts in modern complex control systems recently. They provide many advantages over conventional point-to-point connections, such as the simplification on installation and maintenance with comparatively low cost and the nature requirement of wireless communication in remote control systems. In practice, limited resource networks are shared by multiple controllers, sensors and actuators, and they may need to serve some other information unrelated to control purpose. Consequently, the control system design in networked control systems should be revised by taking communication constraints, for example, finite precision data, time delay and noise in transmission, into account. This thesis studies the robust control and state estimation of uncertain systems, when feedback information is sent via limited capacity communication channels. It focuses on the problem of finite precision data due to the communication constraints. The proposed schemes are based on the robust set-valued state estimation and the optimal control techniques. A state estimation problem of linear uncertain system is studied first. In this problem, we propose an algorithm called coder-decoder for uncertain systems. The coder encodes the observed output into a finite-length codeword and sends it to the decoder that generates the estimated state based on the received codeword. As an illustration, we apply the results in state estimation problem to a precision missile guidance problem using sensor fusion. In this problem, the information obtained from remote sensors is transmitted through limited capacity communication networks to the guided missile. Next, we study a stabilization problem of linear uncertain systems with state feedback. In this problem, the coder-controller scheme is developed to asymptotically stabilize the uncertain systems via limited capacity communication channels. The coder encodes the full state variable into a finite-length codeword and sends it to the controller that drives the system state to the origin. To achieve the asymptotic stability, we use a dynamic quantizer so that quantization noise converges to zero. The results in both state estimation and stabilization problems can handle the problem of finite data rate communication networks in control systems.

Telecommunication networks become major parts in modern complex control systems recently. They provide many advantages over conventional point-to-point connections, such as the simplification on installation and maintenance with comparatively low cost and the nature requirement of wireless communication in remote control systems. In practice, limited resource networks are shared by multiple controllers, sensors and actuators, and they may need to serve some other information unrelated to control purpose. Consequently, the control system design in networked control systems should be revised by taking communication constraints, for example, finite precision data, time delay and noise in transmission, into account. This thesis studies the robust control and state estimation of uncertain systems, when feedback information is sent via limited capacity communication channels. It focuses on the problem of finite precision data due to the communication constraints. The proposed schemes are based on the robust set-valued state estimation and the optimal control techniques. A state estimation problem of linear uncertain system is studied first. In this problem, we propose an algorithm called coder-decoder for uncertain systems. The coder encodes the observed output into a finite-length codeword and sends it to the decoder that generates the estimated state based on the received codeword. As an illustration, we apply the results in state estimation problem to a precision missile guidance problem using sensor fusion. In this problem, the information obtained from remote sensors is transmitted through limited capacity communication networks to the guided missile. Next, we study a stabilization problem of linear uncertain systems with state feedback. In this problem, the coder-controller scheme is developed to asymptotically stabilize the uncertain systems via limited capacity communication channels. The coder encodes the full state variable into a finite-length codeword and sends it to the controller that drives the system state to the origin. To achieve the asymptotic stability, we use a dynamic quantizer so that quantization noise converges to zero. The results in both state estimation and stabilization problems can handle the problem of finite data rate communication networks in control systems.

Telecommunication networks become major parts in modern complex control systems recently. They provide many advantages over conventional point-to-point connections, such as the simplification on installation and maintenance with comparatively low cost and the nature requirement of wireless communication in remote control systems. In practice, limited resource networks are shared by multiple controllers, sensors and actuators, and they may need to serve some other information unrelated to control purpose. Consequently, the control system design in networked control systems should be revised by taking communication constraints, for example, finite precision data, time delay and noise in transmission, into account. This thesis studies the robust control and state estimation of uncertain systems, when feedback information is sent via limited capacity communication channels. It focuses on the problem of finite precision data due to the communication constraints. The proposed schemes are based on the robust set-valued state estimation and the optimal control techniques. A state estimation problem of linear uncertain system is studied first. In this problem, we propose an algorithm called coder-decoder for uncertain systems. The coder encodes the observed output into a finite-length codeword and sends it to the decoder that generates the estimated state based on the received codeword. As an illustration, we apply the results in state estimation problem to a precision missile guidance problem using sensor fusion. In this problem, the information obtained from remote sensors is transmitted through limited capacity communication networks to the guided missile. Next, we study a stabilization problem of linear uncertain systems with state feedback. In this problem, the coder-controller scheme is developed to asymptotically stabilize the uncertain systems via limited capacity communication channels. The coder encodes the full state variable into a finite-length codeword and sends it to the controller that drives the system state to the origin. To achieve the asymptotic stability, we use a dynamic quantizer so that quantization noise converges to zero. The results in both state estimation and stabilization problems can handle the problem of finite data rate communication networks in control systems.

This thesis contains two essays that use state-of-the-art econometric methods to estimate the implicit prices of various housing and vehicle attributes in hedonic price analysis. The additive nonparametric regression proposed by Hastie and Tibshirani (1990) is applied to capture a series of nonlinearities relating prices to their attributes that cannot be captured by conventional parametric approach. Due to its additive structure, the additive nonparametric regression retains an important interpretative feature of the linear model and avoids the drawbacks of a fully nonparametric design such as slow rates of convergence and the "curse of dimensionality." The "benchmark" parametric specification for the hedonic price function is carefully chosen via the estimation of the Box and Cox (1964) and Wooldridge (1992) transformations. The additive nonparametric model provides smaller price prediction errors than the benchmark parametric specification in standard goodness of fit measures. The first study examines the effects on housing prices of the structural and environmental attributes using residential sales data from Portland, Oregon. The overall estimation results verify that most housing attributes that are generally linked to the perception of quality, such as larger total structure square footage and higher elevation, have significant positive implicit prices. Attributes that reduce house quality, such as age of house and distance to environmental amenities, discount the value of a house. Complex price effects of various housing attributes are revealed by the additive nonparametric regression. The second study uses a hedonic price approach to estimate the effects on used car prices of vehicle emission attributes, such as hydrocarbon and carbon monoxide emissions, using data from the Vehicle Inspection Program in Portland, Oregon. The estimation results show that used car value is on average higher for vehicles with lower hydrocarbon and carbon monoxide emissions, ceteris paribus. This empirical finding is consistent with recent reports from the U.S. Environmental Protection Agency, which indicate that used vehicles failing to pass required emission tests face potentially high repair costs and frequent smog-check requirements. More cylinders and larger engine size are highly valued. Higher mileage receives relatively little discount compared to age of vehicle. / Graduation date: 2000

The relative merits of the Fisher linear discriminant function (Efron, 1975) and logistic regression procedure (Press and Wilson, 1978; McLachlan and Byth, 1979), applied to the two group discrimination problem under conditions of multivariate normality and common covariance, have been debated. In related research, DiPillo (1976, 1977, 1979) has argued that a biased Fisher linear discriminant function is preferable when one or more collinearities exist among the classifying variables. This paper proposes a generalized ridge logistic regression (GRL) estimator as a logistic analog to DiPillo's biased alternative estimator. Ridge and Principal Component logistic estimators proposed by Schaefer et al. (1984) for conventional logistic regression are shown to be special cases of this generalized ridge logistic estimator. Two Fisher estimators (Linear Discriminant Function (LDF) and Biased Linear Discriminant Function (BLDF)) and three logistic estimators (Linear Logistic Regression (LLR), Ridge Logistic Regression (RLR) and Principal Component Logistic Regression (PCLR)) are compared in a Monte Carlo simulation under varying conditions of distance between populations, training set s1ze and degree of collinearity. A new approach to the selection of the ridge parameter in the BLDF method is proposed and evaluated. The results of the simulation indicate that two of the biased estimators (BLDF, RLR) produce smaller MSE values and are more stable estimators (smaller standard deviations) than their unbiased counterparts. But the improved performance for MSE does not translate into equivalent improvement in error rates. The expected actual error rates are only marginally smaller for the biased estimators. The results suggest that small training set size, rather than strong collinearity, may produce the greatest classification advantage for the biased estimators. The unbiased estimators (LDF, LLR) produce smaller average apparent error rates. The relative advantage of the Fisher estimators over the logistic estimators is maintained. But, given that the comparison is made under conditions most favorable to the Fisher estimators, the absolute advantage of the Fisher estimators is small. The new ridge parameter selection method for the BLDF estimator performs as well as, but no better than, the method used by DiPillo. The PCLR estimator shows performance comparable to the other estimators when there is a high level of collinearity. However, the estimator gives up a significant degree of performance in conditions where collinearity is not a problem. / Graduation date: 1991

Thesis (M.S.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 32-33). Also available on the World Wide Web.