Thesis (M. Phil.)--University of Hong Kong, 1988.

Thesis (M.S.)--Rochester Institute of Technology, 1984. / Typescript. Includes bibliographical references (leaf 30).

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering, 2018 / Trans-radial amputees struggle daily when it comes to performing one or more of their activities of daily living (ADLs). Myoelectric prosthetic hands have recently been developed to a point where they can assist trans-radial amputees to perform their ADLs,making use of electromyographic (EMG) signals to drive the prosthetic hand. In order to function, a myoelectric prosthetic hand requires multiple electrodes to collect EMG data (denoted a channel) remaining forearm muscles, aswell as complex classification algorithms to process the data in real time. The focus of research in this field is directed at developing or improving the classification algorithms, often ignoring the optimisation of the EMG electrodes themselves. The electrodes can be optimised either by position or number, however in research where electrodes are optimised, classification accuracy is used as a measure of success for the optimisation, which requires optimisation of the classification algorithm itself. The focus of the current study was to develop a method that could optimise the EMG electrode placements and number, without needing a classification algorithm. A pre-existing 8-EMG channel dataset for seven subjects was used. The experimental method involved generating combinations of two, three and four channels from which optimal channel combinations were selected. The optimisation process made use of principal component analysis (PCA), which generated a reduced-quality model for each potential combination. The reduced-quality and original models were compared, and the optimal channel combinations identified from those comparisons with the least error. The success of the optimisation was defined as the impact that a reduced number of EMG channels would have on the percentage of variance retained (PVR) by the optimal channel combinations. The optimal channels for each subject were compared, and although each subject displayed variation, in general the important channels were identified as those that were located over the Extensor digitorum (ED), Flexor pollicis longus (FPL), Flexor digitorum superficialis (FDS), Flexor digitorum profundis (FDP), and iii Extensor carpi ulnaris (ECU) muscles. The optimal channel combinations for all subjects together had an average of 64.5% PVR for the 2-channel setup, 73.9% for the 3-channel setup, and 76.5% for the 4-channel setup. This shows that it is possible to reduce the number of channels and retain a large amount of variance in the data without the use of classification algorithms. / XL2019

This thesis introduces the application of discrete Principal Component Analysis (PCA) to corporate governance research. Given the presence of many discrete variables in typical governance studies, I argue that this method is superior to standard PCA that has been employed by others working in the area. Using a dataset of 244 companies listed on the London Stock Exchange in the year 2002-2003, I find that Pearson's correlations underestimate the strength of association between two variables, when at least one of them is discrete. Accordingly, standard PCA performed on the Pearson correlation matrix results in biased estimates. Applying discrete PCA on the polychoric correlation matrix, I extract from 28 corporate governance variables 10 significant factors. These factors represent 8 main aspects of the governance system, namely auditor reputation, large shareholder influence, size of board committees, social responsibility, risk optimisation, director independence level, female representation and institutional ownership. Finally, I investigate the relationship between corporate governance and a firm's long-run share market performance, with the former being the factors extracted. Consistent with Demsetz' (1983) argument, I document limited explanatory power for these governance factors.

Thesis (Ph. D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 278-292).

Thesis (M.S.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains vi, 67 p. : ill. (some col.), col. maps. Includes abstract. Includes bibliographical references (p. 65-67).

Thesis (Ph. D.)--Lehigh University, 2006. / Includes vita. Includes bibliographical references (leaves 163-173).

In principal component analysis (PCA), the principal components (PC) are linear combinations of the variables that minimize some objective function. In the classical setup the objective function is the variance of the PC's. The variance of the PC's can be easily upset by outlying observations; hence, Chen and Li (1985) proposed a robust alternative for the PC's obtained by replacing the variance with an M-estimate of scale. This approach cannot achieve a high breakdown point (BP) and efficiency at the same time. To obtain both high BP and efficiency, we propose to use MM- and τ-estimates in place of the M-estimate. Although outliers may cause bias in both the direction and the size of the PC's, Chen and Li looked at the scale bias only, whereas we consider both. All proposed robust methods are based on the minimization of a non-convex objective function; hence, a good initial starting point is required. With this in mind, we propose an orthogonal version of the least median of squares (Rousseeuw and Leroy, 1987) and a new method that is orthogonal equivariant, robust and easy to compute. Extensive Monte Carlo study shows promising results for the proposed method. Orthogonal regression and detection of multivariate outliers are discussed as possible applications of PCA. / Science, Faculty of / Statistics, Department of / Graduate

Motivated by dimension reduction in regression analysis and signal detection, we investigate order determination for large dimensional matrices with spiked structures in which the dimensions of the matrices are proportional to the sample sizes. Because the asymptotic behaviors of the estimated eigenvalues differ completely from those in fixed dimension scenarios, we then discuss the largest possible order, say q, we can identify and introduce criteria for different settings of q. When q is assumed to be fixed, we propose a "valley-cliff" criterion with two versions - one based on the original differences of eigenvalues and the other based on the transformed differences - to reduce the effect of ridge selection in the criterion. This generic method is very easy to implement and computationally inexpensive, and it can be applied to various matrices. As examples, we focus on spiked population models, spiked Fisher matrices and factor models with auto-covariance matrices. For the case of divergent q, we propose a scale-adjusted truncated double ridge ratio (STDRR) criterion, where a scale adjustment is implemented to deal with the bias in scale parameter for large q. Again, examples include spiked population models, spiked Fisher matrices. Numerical studies are conducted to examine the finite sample performances of the method and to compare it with existing methods. As for theoretical contributions, we investigate the limiting properties, including convergence in probability and central limit theorems, for spiked eigenvalues of spiked Fisher matrices with divergent q. Keywords: Auto-covariance matrix, factor model, finite-rank perturbation, Fisher matrix, principal component analysis (PCA), phase transition, random matrix theory (RMT), ridge ratio, spiked population model.

published_or_final_version / Real Estate and Construction / Doctoral / Doctor of Philosophy