Wenyang Zhang. / "October 1998." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (p. 190-196). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

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Receiver operating characteristic (ROC) analysis is one of the most widely used methods in evaluating the accuracy of a classification method. It is used in many areas of decision making such as radiology, cardiology, machine learning as well as many other areas of medical sciences. The dissertation proposes a novel nonparametric estimation method of the ROC surface for the three-class classification problem via Bernstein polynomials. The proposed ROC surface estimator is shown to be uniformly consistent for estimating the true ROC surface. In addition, it is shown that the map from which the proposed estimator is constructed is Hadamard differentiable. The proposed ROC surface estimator is also demonstrated to lead to the explicit expression for the estimated volume under the ROC surface . Moreover, the exact mean squared error of the volume estimator is derived and some related results for the mean integrated squared error are also obtained. To assess the performance and accuracy of the proposed ROC and volume estimators, Monte-Carlo simulations are conducted. Finally, the method is applied to the analysis of two real data sets.

Lai, Chu Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 44-46). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- B-Spline Modeling of Nonparametric Fixed Effects --- p.3 / Chapter 3 --- Parameter Estimation --- p.5 / Chapter 3.1 --- Fixed Component Estimation using Adaptive Group Lasso --- p.5 / Chapter 3.2 --- Random Component Estimation using Newton Raphson --- p.7 / Chapter 3.3 --- Combining the Two Algorithms --- p.9 / Chapter 4 --- Selection of Model Complexity --- p.10 / Chapter 4.1 --- Model Selection Criterion --- p.10 / Chapter 4.2 --- Calculating the Degrees of Freedom --- p.10 / Chapter 4.3 --- Practical Minimization of (4.1) --- p.12 / Chapter 5 --- Theoretical results / Chapter 5.1 --- Consistency of adaptive group lasso --- p.14 / Chapter 5.2 --- Consistency of Bayesian Information Criterion --- p.16 / Chapter 6 --- Simulations / Chapter 7 --- Real applications / Chapter 7.1 --- Prostate cancer data --- p.23 / Chapter 7.2 --- Housing data --- p.25 / Chapter 7.3 --- Depression Dataset --- p.27 / Chapter 8 --- Summary --- p.31 / Chapter A --- Derivation of (3.7) and (3.8) --- p.32 / Chapter B --- Lemmas --- p.34 / Chapter C --- Proofs of theorems --- p.37

This dissertation is composed of three essays regarding the finite sample properties of estimators for nonparametric models. In the first essay we investigate the finite sample performances of four estimators for additive nonparametric regression models - the backfitting B-estimator, the marginal integration M-estimator and two versions of a two stage 2S-estimator, the first proposed by Kim, Linton and Hengartner (1999) and the second which we propose in this essay. We derive the conditional bias and variance of the 2S estimators and suggest a procedure to obtain optimal bandwidths that minimize an asymptotic approximation of the mean average squared errors (AMASE). We are particularly concerned with the performance of these estimators when bandwidth selection is done based on data driven methods. We compare the estimators' performances based on various bandwidth selection procedures that are currently available in the literature as well as with the procedures proposed herein via a Monte Carlo study. The second essay is concerned with some recently proposed kernel estimators for panel data models. These estimators include the local linear estimator, the quasi-likelihood estimator, the pre-whitening estimators, and the marginal kernel estimator. We focus on the finite sample properties of the above mentioned estimators on random effects panel data models with different within-subject correlation structures. For each estimator, we use the asymptotic mean average squared errors (AMASE) as the criterion function to select the bandwidth. The relative performance of the test estimators are compared based on their average squared errors, average biases and variances. The third essay is concerned with the finite sample properties of estimators for nonparametric regression models with autoregressive errors. The estimators studied are: the local linear, the quasi-likelihood, and two pre-whitening estimators. Bandwidths are selected based on the minimization of the asymptotic mean average squared errors (AMASE) for each estimator. Two regression functions and multiple variants of autoregressive processes are employed in the simulation. Comparison of the relative performances is based mainly on the estimators' average squared errors (ASE). Our ultimate objective is to provide an extensive finite sample comparison among competing estimators with a practically selected bandwidth. / Graduation date: 2006

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 131-134).

Thesis--M. Phil., University of Hong Kong, 1982.

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Semiparametric and nonparametric estimators are becoming indispensable tools in applied econometrics. Many of these estimators depend on the choice of smoothing bandwidth and kernel function. Optimality of such parameters is determined by unobservable smoothness of the model, that is, by differentiability of the distribution functions of random variables in the model. In this thesis we consider two estimators of this class: the smoothed maximum score estimator for binary choice models and the kernel density estimator. / We present theoretical results on the asymptotic distribution of the estimators under various smoothness assumptions and derive the limiting joint distributions for estimators with different combinations of bandwidths and kernel functions. Using these nontrivial joint distributions, we suggest a new way of improving accuracy and robustness of the estimators by considering a linear combination of estimators with different smoothing parameters. The weights in the combination minimize an estimate of the mean squared error. Monte Carlo simulations confirm suitability of this method for both smooth and non-smooth models. / For the original and smoothed maximum score estimators, a formal procedure is introduced to test for equivalence of the maximum likelihood estimators and these semiparametric estimators, which converge to the true value at slower rates. The test allows one to identify heteroskedastic misspecifications in the logit/probit models. The method has been applied to analyze the decision of married women to join the labour force.