In regression with near collinear explanatory variables, the least squares predictor has large variance. Ordinary least squares regression (OLSR) often leads to unrealistic regression coefficients. Several regularized regression methods have been proposed as alternatives. Well-known are principal components regression (PCR), ridge regression (RR) and continuum regression (CR). The latter two involve a continuous metaparameter, offering additional flexibility. For a univariate response variable, CR incorporates OLSR, PLSR, and PCR as special cases, for special values of the metaparameter. CR is also closely related to RR. However, CR can in fact yield regressors that vary discontinuously with the metaparameter. Thus, the relation between CR and RR is not always one-to-one. We develop a new class of regression methods, LSRR, essentially the same as CR, but without discontinuities, and prove that any optimization principle will yield a regressor proportional to a RR, provided only that the principle implies maximizing some function of the regressor's sample correlation coefficient and its sample variance. For a multivariate response vector we demonstrate that a number of well-established regression methods are related, in that they are special cases of basically one general procedure. We try a more general method based on this procedure, with two meta-parameters. In a simulation study we compare this method to ridge regression, multivariate PLSR and repeated univariate PLSR. For most types of data studied, all methods do approximately equally well. There are cases where RR and LSRR yield larger errors than the other methods, and we conclude that one-factor methods are not adequate for situations where more than one latent variable are needed to describe the data. Among those based on latent variables, none of the methods tried is superior to the others in any obvious way.

In indoor environment, the multi-sensor system can be used as an efficient solution for target location process, in terms of lower estimation cost, due to the factor that sensors have the advantages of low power, simple, cheap, and low operation complexity. However, the location methods and the placements of designed multisensor have great impact on the location performance. Based on the time difference of arrival (TDOA), the present research utilizes linear-correction spherical-interpolation (LCSI) method to estimate the location of its targets. The method is a combination of the linear-correction least-squares method and the spherical-interpolation method. Apart from the usual process of iterative, nonlinear minimization, and consequently, under the influence of noise interference and target-sensor geometry, the spherical-interpolation method will produce better results; therefore, SI method is used in place of the LS part of the LCLS method and named as the LCSI method. The objective is to correct the SI method to generate a better estimate performance. In addition to the performance issues, the limitation of the methods will also be examined. The geometric dilution of precision (GDOP) of the TDOA location method in the 3-D scenario is demonstrated with the effects on location performance of both inside and outside of the multi-sensor formation. Programmed 3-D scenario are used in the simulations, where cases with three different multiple sensor formations and two different target heights are investigated. From the simulation results of various location methods, it can be seen that LCSI has has its advantages over other methods in the wireless TDOA location.

Support for the use of progress monitoring results for high-stakes decisions is emerging in the literature, but few studies support the reliability of the measures for this level of decision-making. What little research exists is limited to oral reading fluency measures, and their reliability for progress monitoring (PM) is not supported. This dissertation explored methods rarely applied in the literature for summarizing and analyzing progress monitoring results for medium- to high-stakes decisions. The study was conducted using extant data from 92 "low performing" third graders who were progress monitored using mathematics concept and application measures. The results for the participants in this study identified 1) the number of weeks needed to reliably assess growth on the measure; 2) if slopes differed when results were analyzed with parametric or nonparametric analyses; 3) the reliability of growth; and 4) the extent to which the group did or did not meet parametric assumptions inherent in the ordinary least square regression model. The results indicate reliable growth from static scores can be obtained in as few as 10 weeks of progress monitoring. It was also found that within this dataset, growth through parametric and nonparametric analyses was similar. These findings are limited to the dataset analyzed in this study but provide promising methods not widely known among practitioners and rarely applied in the PM literature.

We consider the application of high-order spectral/hp finite element technology to the numerical solution of boundary-value problems arising in the fields of fluid and solid mechanics. For many problems in these areas, high-order finite element procedures offer many theoretical and practical computational advantages over the low-order finite element technologies that have come to dominate much of the academic research and commercial software of the last several decades. Most notably, we may avoid various forms of locking which, without suitable stabilization, often plague low-order least-squares finite element models of incompressible viscous fluids as well as weak-form Galerkin finite element models of elastic and inelastic structures. The research documented in this dissertation includes applications of spectral/hp finite element technology to an analysis of the roles played by the linearization and minimization operators in least-squares finite element models of nonlinear boundary value problems, a novel least-squares finite element model of the incompressible Navier-Stokes equations with improved local mass conservation, weak-form Galerkin finite element models of viscoelastic beams and a high-order seven parameter continuum shell element for the numerical simulation of the fully geometrically nonlinear mechanical response of isotropic, laminated composite and functionally graded elastic shell structures. In addition, we also present a simple and efficient sparse global finite element coefficient matrix assembly operator that may be readily parallelized for use on shared memory systems. We demonstrate, through the numerical simulation of carefully chosen benchmark problems, that the finite element formulations proposed in this study are efficient, reliable and insensitive to all forms of numerical locking and element geometric distortions.

Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts. Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems. Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy. Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.

Jag använder ett från Världsbanken nyligen utkommet datamaterial över institutionell kvalitet i världens länder för att i en replikeringsstudie undersöka sambandet mellan institutionell utveckling och ekonomisk tillväxt. Modellen har med framgång redan tidigare använts, men i detta arbete är tidsperioden en senare och datamaterialet enligt min bedömning av högre kvalitet. För att kunna göra det senare uttalandet och analysera resultaten på ett uttömmande sätt, innefattar arbetet en översiktlig presentation av institutionella teorier. Eftersom undersökt samband i utgångsläget antas uppvisa dubbelriktad kausalitet, använder jag ett ekonometriskt tillvägagångssätt innehållande instrumentering för att trygga validiteten. Sammantaget visar resultaten en enkelriktad, positiv kausaleffekt från institutionell kvalitet till ekonomisk tillväxt. Det är en bit kvar till en verkligt fruktbar modellkonstruktion, samtidigt som arbetet pekar på att institutioner hör hemma i en sådan.

In this thesis a machine vision based indoor navigation system is presented. This is achieved by using rotationally independent optimized color reference labels and a geometrical camera calibration model which determines a set of camera parameters. All reference labels carry one byte of information (0 to 255), which can be designed for different values. An algorithm in Matlab has been developed so that a machine vision system for N number of symbols can recognize the symbols at different orientations. A camera calibration model describes the mapping between the 3-D world coordinates and the 2-D image coordinates. The reconstruction system uses the direct linear transform (DLT) method with a set of control reference labels in relation to the camera calibration. The least-squares adjustment method has been developed to calculate the parameters of the machine vision system. In these experiments it has been demonstrated that the pose of the camera can be calculated, with a relatively high precision, by using the least-squares estimation.

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results.<p> A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification.<p> In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design.

Power systems are protected by numerical relays that detect and isolate faults that may occur on power systems. The correct operation of the relay is very important to maintain the security of the power system. <p>Numerical relays that use voltage measurements from the power system provided by coupling capacitor voltage transformers (CCVT) have sometimes difficulty in correctly identifying a fault in the protected area. The fundamental frequency voltage phasor resulting from these CCVT measurements may result in a deviation from the true value and therefore may locate this phasor temporarily in the incorrect operating region. This phasor deviation is due to the CCVT behavior and the CCVT introduces spurious decaying and oscillating transient signal components on top of the original voltage received from the power system in response to sudden voltage changes produced during faults. Most of the existing methods for estimating the voltage phasor do not take advantage of the knowledge of the CCVT behavior that can be obtained from its design parameters.<p>A new least squares error method for phasor estimation is presented in this thesis, which improves the accuracy and speed of convergence of the phasors obtained, using the knowledge of the CCVT behavior. The characteristics of the transient signal components introduced by the CCVT, such as frequencies and time constants of decay, are included in the description of the curve to be fitted, which is required in a least squares fitting technique. Parameters such as window size and sampling rate for optimum results are discussed.<p>The method proposed is evaluated using typical power systems, with results that can be compared to the response if an ideal potential transformer (PT) were used instead of a CCVT. The limitations of this method are found in some specific power system scenarios, where the natural frequencies of the power system are close to that of the CCVT, but with longer time constants. The accuracy with which the CCVT parameters are known is also assessed, with results that show little impact compared to the improvements achievable.

University of Macau / Faculty of Science and Technology / Department of Electromechanical Engineering