Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Florida, 1983. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaf 83).

Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Iowa, 2007. / Supervisors: George Woodworth, Matthew Bognar. Includes bibliographical references (leaves 72-73).

Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (May 2, 2007) Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 107-111).

This thesis develops some new di.erence-based methods for nonparametric regression models. The .rst part of this thesis focuses on the variance estimation for nonparametric models with various settings. In Chapter 2, a uni.ed framework of variance estimator is proposed for a model with smooth mean function. This framework combines the higher order di.erence sequence with least squares method and greatly extends the literature, including most of existing methods as special cases. We derive the asymp­totic mean squared errors and make both theoretical and numerical comparison for various estimators within the system. Based on the dramatic interaction of ordinary di.erence sequences and least squares method, we eventually .nd a uniformly sat­isfactory estimator for all the settings, solving the challenging problem of sequence selection. In Chapter 3, three methods are developed for the variance estimation in the repeated measurement setting. Both their asymptotic properties and .nite sample performance are explored. The sequencing method is shown to be the most adaptive while the sample variance method and the partitioning method are shown to outperform in certain cases. In Chapter 4, we propose a pairwise regression method for estimating the residual variance. Speci.cally, we regress the squared di.erence between observations on the squared distance between design points, and then es­timate the residual variance as the intercept. Unlike most existing di.erence-based estimators that require a smooth regression function, our method applies to regres­sion models with jump discontinuities. And it also applies to the situations where the design points are unequally spaced. The smoothness assumption of the nonparametric regression function is quite critical for the curve .tting and the residual variance estimation. The second part (Chapter 5) concentrates on the discontinuities detection for the mean function. In particular, we revisit the di.erence-based method in M¨uller and Stadtm¨uller (1999) and propose to improve it. To achieve the goal, we .rst reveal that their method is less e.cient due to the inappropriate choice of the response variable in their linear regression model. We then propose a new regression model for estimating the resid­ual variance and the total amount of discontinuities simultaneously. In both theory and simulations, we show that the proposed variance estimator has a smaller MSE compared to their estimator, whereas the e.ciency of the estimators for the total amount of discontinuities remain unchanged. Finally, we construct a new test proce­dure for detection using the newly proposed estimations; and via simulation studies, we demonstrate that our new test procedure outperforms the existing one in most settings. At the beginning of Chapter 6, a series of new di.erence sequences is de.ned to complete the span between the optimal sequence and the ordinary sequence. The vari­ance estimators using proposed sequences are shown to be quite robust and achieve smallest mean square errors for most of general settings. Then, the di.erence-based methods for variance function estimation are generally discussed. Keywords: Asymptotic normality, Di.erence-based estimator, Di.erence sequence, Jump point, Least square, Nonparametric regression, Pairwise regression, Repeated measurement, Residual variance

The semi-parametric model enjoys a relatively flexible structure and keeps some of the simplicity in the statistical analysis. Hence, there are abundance discussions on semi-parametric models in the literature. The concept of partial consistency was firstly brought up in Neyman and Scott (1948). It was said the in cases where infinite parameters are involved, consistent estimators are always attainable for those "structural" parameters. The "structural' parameters are finite and govern infinite samples. Since the nonparametric model can be regarded as a parametric model with infinite parameters, then the semi-parametric model can be easily transformed into a infinite-parametric model with some "structural" parameters. Therefore, based on this idea, we develop several new methods for the estimating and model checking problems in semi-parametric models. The implementation of applying partial consistency is through the method "local average". We consider the nonparametric part as piecewise constant so that infinite parameters are created. The "structural" parameters shall be the parametric part, the model residual variance and so on. Due to the partial consistency phenomena, classical statistic tools can then be applied to obtain consistent estimators for those "structural" parameters. Furthermore, we can take advantage of the rest of parameters to estimate the nonparametric part. In this thesis, we take the varying coefficient model as the example. The estimation of the functional coefficient is discussed and relative model checking methods are presented. The proposed new methods, no matter for the estimation or the test, have remarkably lessened the computation complexity. At the same time, the estimators and the tests get satisfactory asymptotic statistical properties. The simulations we conducted for the new methods also support the asymptotic results, giving a relatively efficient and accurate performance. What's more, the local average method is easy to understand and can be flexibly applied to other type of models. Further developments could be done on this potential method. In Chapter 2, we introduce a local average method to estimate the functional coefficients in the varying coefficient model. As a typical semi-parametric model, the varying coefficient model is widely applied in many areas. The varying coefficient model could be seen as a more flexible version of classical linear model, while it explains well when the regression coefficients do not stay constant. In addition, we extend this local average method to the semi-varying coefficient model, which consists of a linear part and a varying coefficient part. The procedures of the estimations are developed, and their statistical properties are investigated. Plenty of simulations and a real data application are conducted to study the performance of the proposed method. Chapter 3 is about the local average method in variance estimation. Variance estimation is a fundamental problem in statistical modeling and plays an important role in the inferences in model selection and estimation. In this chapter, we have discussed the problem in several nonparametric and semi-parametric models. The proposed method has the advantages of avoiding the estimation of the nonparametric function and reducing the computational cost, and can be easily extended to more complex settings. Asymptotic normality is established for the proposed local average estimators. Numerical simulations and a real data analysis are presented to illustrate the finite sample performance of the proposed method. Naturally, we move to the model checking problem in Chapter 4, still taking varying coefficient models as an example. One important and frequently asked question is whether an estimated coefficient is significant or really "varying". In the literature, the relative hypothesis tests usually require fitting the whole model, including the nuisance coefficients. Consequently, the estimation procedure could be very compute-intensive and time-consuming. Thus, we bring up several tests which can avoid unnecessary functions estimation. The proposed tests are very easy to implement and their asymptotic distributions under null hypothesis have been deduced. Simulations are also studied to show the properties of the tests.

In this study I explore the feminist critique of Reinhold Niebuhr’s theology of sin, both to understand what the Niebuhrian and feminist understandings of sin talk about, and to see whether or not, or to what extent they are tenable in theory and in practice. Niebuhr’s feminist critics argue that Niebuhr’s claim of pride as the primary human sin fits only with men’s experience; women’s sin, they contend, is not self-inflation but self-loss. While I acknowledge the value of Niebuhr’s feminist critics’ interpretation of sin, this study provides a Niebuhrian response to the feminist critique. My main contention is that by overemphasizing women’s sin of passivity, some feminist theologians go too far to deny women’s capability of committing sin actively against others and the divine in both socio-moral and religio-theological aspect. The total rejection of the applicability of pride to women’s situation, I contend, undermines the profoundness of the feminist critique. I firstly give detailed expositions of Niebuhr’s theology of sin and the feminist critique of Niebuhr’s theology of sin respectively. The main discrepancies between the Niebuhrian and feminist understandings of sin will be laid out. Then I respond to some feminist criticisms by pointing out that the feminist misreading of Niebuhr on the topics of pride, the self, love, justice and the family is prevalent. I also question the two presuppositions of the feminist critique—the idea of women’s innocence and the spirit of secularity. These two presuppositions, I argue, contain in them some insoluble dilemmas that cause trouble for understanding women’s secular and religious experience. Lastly, I try to pull the insights of Niebuhr and his feminist critics together to form a more integrated view of women’s sin