Master of Science / Department of Statistics / Weixing Song / In the classical Tobit regression model, the regression error term is often assumed to have a zero mean normal distribution with unknown variance, and the regression function is assumed to be linear. If the normality assumption is violated, then the commonly used maximum likelihood estimate becomes inconsistent. Moreover, the likelihood function will be very complicated if the regression function is nonlinear even the error density is normal, which makes the maximum likelihood estimation procedure hard to implement. In the full nonparametric setup when both the regression function and the distribution of the error term [epsilon] are unknown, some nonparametric estimators for the regression function has been proposed. Although the assumption of knowing the distribution is strict, it is a widely adopted assumption in Tobit regression literature, and is also confirmed by many empirical studies conducted in the econometric research. In fact, a majority of the relevant research assumes that [epsilon] possesses a normal distribution with mean 0 and unknown standard deviation. In this report, we will try to develop a semi-parametric estimation procedure for the regression function by assuming that the error term follows a distribution from a class of 0-mean symmetric location and scale family. A minimum distance estimation procedure for estimating the parameters in the regression function when it has a specified parametric form is also constructed. Compare with the existing semiparametric and nonparametric methods in the literature, our method would be more efficient in that more information, in particular the knowledge of the distribution of [epsilon], is used. Moreover, the computation is relative inexpensive. Given lots of application does assume that [epsilon] has normal or other known distribution, the current work no doubt provides some more practical tools for statistical inference in Tobit regression model.

A new specialist design role is emerging in the construction industry. The primary task related to this role is focused on the control, development and sharing of geometric information with members of the design team in order to develop a design solution. Individuals engaged in this role can be described as a parametric designers. Parametric design involves the exploration of multiple solutions to architectural design problems using parametric models. In the past these models have been defined by computer programs, nowcommercially available parametric software provides a simpler means of creating these models. It is anticipated that the emergence of parametric designers will spread and a deeper understanding of the role is required. This thesis is aimed at establishing a detailed understanding of the tasks related to this new specialism and to develop a set of considerations that should be made when undertaking these tasks. The position of the parametric designer in architectural practice presents new opportunities in the design process this thesis also aims to capture these. Developments in this field of design are driven by practice. It is proposed that a generalised understanding of applied parametric design is primarily developed through the study of practical experience. Two bodies of work inform this study. First, a detailed analytical review of published work that focuses on the application of parametric technology and originatesfrompractice. This material concentrates on the documentation of case studies from a limited number of practices. Second, a series of case studies involving the author as participant and observer in the context of contemporary practice. This primary research of applied use of parametric tools is documented in detail and generalised findings are extracted. Analysis of the literature from practice and generalisations based on case studies is contrasted with a review of relevant design theory. Based on this, a series of strategies for the parametric designer are identified and discussed.

Vita. / Digitized by Kansas Correctional Industries

Semiconductor manufacturers must ensure that chips conform to their specifications before they are shipped to customers. This is achieved by testing various parameters of a chip to determine whether it is defective or not. Separating defective chips from fault-free ones is relatively straightforward for functional or other Boolean tests that produce a go/no-go type of result. However, making this distinction is extremely challenging for parametric tests. Owing to continuous distributions of parameters, any pass/fail threshold results in yield loss and/or test escapes. The continuous advances in process technology, increased process variations and inaccurate fault models all make this even worse. The pass/fail thresholds for such tests are usually set using prior experience or by a combination of visual inspection and engineering judgment. Many chips have parameters that exceed certain thresholds but pass Boolean tests. Owing to the imperfect nature of tests, to determine whether these chips (called "outliers") are indeed defective is nontrivial. To avoid wasted investment in packaging or further testing it is important to screen defective chips early in a test flow. Moreover, if seemingly strange behavior of outlier chips can be explained with the help of certain process parameters or by correlating additional test data, such chips can be retained in the test flow before they are proved to be fatally flawed. In this research, we investigate several methods to identify true outliers (defective chips, or chips that lead to functional failure) from apparent outliers (seemingly defective, but fault-free chips). The outlier identification methods in this research primarily rely on wafer-level spatial correlation, but also use additional test parameters. These methods are evaluated and validated using industrial test data. The potential of these methods to reduce burn-in is discussed.

Small animal positron emission tomography (PET) image analysis can be particularly challenging with heavily-lesioned animal disease models with limited tracer uptake such as the 6-hydroxydopamine (OHDA) lesioned rat model of Parkinson's disease. Methodology-related variations in measured values of 10% or 15% can obscure meaningful biological differences, so accurate analysis methods are essential. However, placing regions of interest (ROIs) on these images without additional guidance is unreliable, and can lead to significant errors in results. To address this problem, this work develops a partly atlas-guided method place ROIs on structures that lack specific binding with presynaptic dopaminergic tracers. The method is tested by correlation of PET binding potential (BP) with autoradiographic binding measurements, and with repeated PET scans of the same subjects, both with the presynaptic tracer ¹¹C-dihydrotetrabenazine (DTBZ). The method is found to produce reliable results. When directly comparing PET images of the same subject to detect changes, it is essential to minimize variations due to analysis method. To this end, a masking method for automated image registration (AIR) of PET images with dopaminergic tracer rat images is developed. Coregistration with AIR and separate ROI placement are compared and tested with repeated scans of the same rat with DTBZ, and are found to be equivalent. Kinetic modelling algorithms may also introduce bias or scatter to binding potentials (BP) calculated from TACs or in parametric images. To determine the optimal method for this step, algorithms for dopaminergic tracers are compared for small animal DTBZ, ¹¹C-methylphenidate (MP), and ¹¹C-raclopride (Rac) data. Among the tested methods is a new variant of the Logan graphical kinetic modelling method, developed in this work, that issignificantly less biased by target tissue TAC noise than the standard Logan approach. The modified graphical method is further compared with the Logan graphical algorithms with added-noise simulations. The simplified reference tissue model (SRTM) is found to have the best method for ROI TAC data, while the modified graphical algorithm may be preferred when generating parametric images.

The classical parametric estimation approach, maximum likelihood, while providing maximally efficient estimators at the correct model, lacks robustness. As a modification of maximum likelihood, Huber (1964) introduced M-estimators, which are very general but often ad hoc. Basu et al. (1998) developed a family of density-based divergences, many of which exhibit robustness. It turns out that maximum likelihood is a special case of this general class of divergence functions, which are indexed by a parameter alpha. Basu noted that only values of alpha in the [0,1] range were of interest -- with alpha = 0 giving the maximum likelihood solution and alpha = 1 the L2E solution (Scott, 2001). As alpha increases, there is a clear tradeoff between increasing robustness and decreasing efficiency. This thesis develops a family of robust location and scale estimators by applying Basu's alpha-divergence function to a multivariate partial density component model (Scott, 2004). The usefulness of alpha values greater than 1 will be explored, and the new estimator will be applied to simulated cases and applications in parametric density estimation and regression.

After experienced two energy crises, the shock of oil price volatility has become more and more critical economically and strategically. In recent years, the phenomena of high demand, high oil production, and high price of oil have resulted in significant impact on economy and people¡¦s welfare in Taiwan. Two major suppliers are Chinese Petroleum Corporation (CPC) and Formosa Petrochemical Corporation (FPC) in Taiwan. Their responsive strategy become more challenging. To discuss this subject deeply, the event study is applied to understand how the differential price strategy influences their operation. Besides, the non-parametric method is also used to analyze the behavior of the competitive price. Empirical results indicate that after taking the measure of remaining price constant, total sales volume of CPC doesn¡¦t increase. In the other hand, total demand of FPC decreases as expected after increasing price. The results also show that CPC¡¦s operation becomes poorer, and FPC¡¦s operation becomes better. The reason behind FPC¡¦s success may be by expanding foreign market timely. However, the statement needs more data to prove it. Finally, two chosen strategic behaviors can¡¦t explain the price setting of unleaded gasoline, but Bertrand¡¦s statement may explain the phenomenon of price-cutting in 98 unleaded gasoline.

We study the Faraday waves with liquid crystal MBBA and oleic acid. When we drive a disc of fluid on a shaker periodically, we find a series of symmetrically regular patterns of standing waves. The pattern variations with the viscosity of fluid, the depth of fluid and the size of the container are studied in this paper. It is noted that novel patterns of pentagon and heptagon are formed in some special parameters. In higher frequency region, patterns form in grid and ring with shorter wavelength of standing waves usually.

Presently, there are a lot of applications of gear sets with skew axes, some of them, especially worm gear sets and hypoid gear sets, are widely used. Take hypoid gear as example, gear sets produced by different gear factories can¡¦t fit to each other. Due to the lacking in common properties among different systems, it is disadvantageous to integrated application of development of gear researches. Therefore, a common mathematical constructive model is necessary to be established. The main content of this thesis is to construct the mathematical parametric model and the partial differential constraint equation according to the rigid-body transformation theory and General Theorem of Conjugate Surfaces. After finding out the solution from the partial differential constraint equation, a new line-contacted type of tooth profile of gear sets with skew axes, quality analyses to the parameters of gear profile rendered are proceeded. Finally, utilize the software of motion simulation to simulate the operating situation of the linear contacted type of gear sets with skew axes constructed, and supply the demonstration of the theory of tooth profile of gear sets and properties of gear sets.

Fiber optical parametric amplifier (FOPA) is undoubtedly one of the most thriving research topics about optical amplifiers during the past decades. The high optical gain, arbitrary gain regions and wavelength conversion with large frequency shift make FOPA outstanding in diverse application areas like the high-speed all-optical communication, wavelength-tunable laser sources and optical imaging systems. Special fiber gain medium and proper pump source are two essential elements in an FOPA setup. As the research interest on FOPAs has recently gradually extended from the conventional 1.5-_m region to the shorter wavelength band at 1 μm, photonic crystal fibers (PCFs) act as the gain media by virtue of their customized dispersion curve and nonlinearity in this band. And the 1-mum laser sources incorporating ytterbium-doped fiber (YDF) as the gain medium have been investigated as well. We prefer all-fiber laser as the pump source not only because of its high output quality but also its compatibility with other fiber systems like FOPA. However, compared with 1.5-_m range, fiber lasers in 1-_m wavelength window have not been fully developed. Most of the laser sources reported in this wavelength range are not all-fiber base. For those few all-fiber reports, the tuning range of the pulsing wavelength is not wide enough, which might limit the performance of the FOPA. In this thesis, we have investigated tunable fiber lasers aiming at becoming the promising pump sources for 1-μm FOPAs. All-fiber lasers with different techniques and operation schemes based on the YDF have been discussed. Tunable ytterbium (Yb) fiber lasers with short pulsed output are important for pulsed-pumped FOPAs in 1 _m. Passive and active mode locking techniques are both commonly employed in short pulse generation. Passive mode-locking laser cavity usually works at the fundamental frequency of the cavity (?MHz) and has the potential to generate ultra-short pulse (? fs) due to its fast recovery time. On the other hand, active mode locking is more agile in terms of the repetition rate, which is synchronized with the external electrical signal. It can be as high as tens of GHz, which is useful for high-speed optical communication, and also can be as low as tens of MHz, which can benefit applications that require high peak power. For an all-fiber mode-locked laser based on YDF, the self-starting of the passive mode locking in 1 _m is more difficult than in 1.5 μm due to the large value of the normal material dispersion in optical fibers in this shorter wavelength range. In this thesis, we have focused on the active mode-locking cavity. Two schemes of actively mode-locked fiber lasers have be demonstrated. One is with a high repetition rate of about 10-GHz at around 1030 nm. The 30-nm tuning range is beneficial to the development of the wavelength-division multiplexing (WDM) technology in the newly developed 1-μm communication band. And on the basis of this scheme, another actively mode-locked fiber laser with a wider tuning range (almost 50 nm) have been achieved by optimizing the length of the YDF inside the cavity. Considering the applications like fiber sensing or spectroscopy where high peak power is more essential and also due to the limitation of our 980-nm pump power, the repetition rate has been lowered down to around 300 MHz in the second scheme. Tunable continuous-wave (CW) fiber lasers in 1 _m have also been discussed. For an all-fiber ring laser cavity, a stable CW output without mode-hopping can be achieved by selecting out single frequency. Various experimental configurations have been proposed for single-longitudinal-mode (SLM) oscillation. We have combined the multiple-ring cavity (MRC) and the saturable absorber in the same fiber laser cavity to facilitate the SLM generation in 1 _m. The tunable CW SLM fiber laser has the potential to build a sweeping source with instantaneous narrow linewidth for optical coherence tomography (OCT) in this range. It can also be utilized as the pump source for CW FOPAs, which is more immune from the walk-off effect between the pulsed pump and the signal, as long as the stimulated Brillouin scattering (SBS) has been suppressed properly. / published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy