It is well known that when the input variables of the linear regression model are subject to noise contamination, the model parameters can not be estimated uniquely. This, in the statistical literature, is referred to as the identifiability problem of the errors-in-variables models. Further, in linear regression there is an explicit assumption of the existence of a single linear relationship. The statistical properties of the errors-in-variables models under the assumption that the noise variances are either known or that they can be estimated are well documented. In many situations, however, such information is neither available nor obtainable. Although under such circumstances one can not obtain a unique vector of parameters, the space, Ω, of the feasible solutions can be computed. Additionally, assumption of existence of a single linear relationship may be presumptuous as well. A multi-equation model similar to the simultaneous-equations models of econometrics may be more appropriate. The goals of this dissertation are the following: (1) To present analytical techniques or algorithms to reduce the solution space, Ω, when any type of prior information, exact or relative, is available; (2) The data covariance matrix, Σ, can be examined to determine whether or not Ω is bounded. If Ω is not bounded a multi-equation model is more appropriate. The methodology for identifying the subsets of variables within which linear relations can feasibly exist is presented; (3) Ridge regression technique is commonly employed in order to reduce the ills caused by collinearity. This is achieved by perturbing the diagonal elements of Σ. In certain situations, applying ridge regression causes some of the coefficients to change signs. An analytical technique is presented to measure the amount of perturbation required to render such variables ineffective. This information can assist the analyst in variable selection as well as deciding on the appropriate model; (4) For the situations when Ω is bounded, a new weighted regression technique based on the computed upper bounds on the noise variances is presented. This technique will result in identification of a unique estimate of the model parameters.

This thesis focuses on estimation and inference for a large class of semiparametric estimands: the class of continuous functionals of regression functions. This class includes a number of estimands derived from causal inference problems, among then the average treatment effect for a binary treatment when treatment assignment is unconfounded and many of its generalizations for non-binary treatments and individualized treatment policies. Chapter 2, based on work with Stefan Wager, introduces the augmented minimax linear es- timator (AMLE), a general approach to the problem of estimating a continuous linear functional of a regression function. In this approach, we estimate the regression function, then subtract from a simple plug-in estimator of the functional a weighted combination of the estimated regression function’s residuals. For this, we use weights chosen to minimize the maximum of the mean squared error of the resulting estimator over regression functions in a chosen neighborhood of our estimated regression function. These weights are shown to be a universally consistent estimator our linear functional’s Riesz representer, the use of which would result in an exact bias correction for our plug- in estimator. While this convergence can be slow, especially when the Riesz representer is highly nonsmooth, the action of these weights on functions in the aforementioned neighborhood imitates that of the Riesz representer accurately even when they are slow to converge in other respects. As a result, we show that under no regularity conditions on the Riesz representer and minimal regularity conditions on the regression function, the proposed estimator is semiparametrically efficient. In simulation, it is shown to perform very well in the context of estimating the average partial effect in the conditional linear model, a simultaneous generalization of the average treatment effect to address continuous-valued treatments and of the partial linear model to address treatment effect heterogeneity. Chapter 3, based on work with Arian Maleki and José Zubizarreta, studies the minimax linear estimator, a simplified version of the AMLE in which the estimated regression function is taken to be zero, for a class of estimands generalizing the mean with outcomes missing at random. We show semiparametric efficiency under conditions that are only slightly stronger than those required for the AMLE. In addition, we bound the deviation of our estimator’s error from the averaged efficient influence function, characterizing the degree to which the first order asymptotic characterization of semiparametric efficiency is meaningful in finite samples. In simulation, this estimator is shown to perform well relative to alternatives in high-noise, small-sample settings with limited overlap between the covariate distribution of missing and nonmissing units, a setting that is challenging for approaches reliant on accurate estimation of either or both of the regression function and the propensity score. Chapter 4 discusses an approach to rounding linear estimators for the targeted average treatment effect into matching estimators. The targeted average treatment effect is a generalization of the average treatment effect and the average treatment effect on the treated units.

Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Abstract An improvement and more accuracy method for spectrum analysis has been achieved in this thesis. There are three major parts in this thesis: the signal parameter estimation, the optimization of spectrum analysis, and the supervision to electric machinery. All these parts suggest the improvement ways to theories and applications of signal process. Parameter estimation is the base of dynamic designs, controls, and supervisions. This thesis infers the complete method to estimate parameters. The method estimates signal parameters in frequency domain. In electric machinery analysis, the most signals can consist of complex exponents. The component parameters include frequency, damping, amplitude, and phase. Basing on the damping existed or not, signals can be classified into two parts: periodic and non-periodic. Each complex exponent component will produce its band on spectrum. This method references the scales with highest amplitudes to estimate exact parameters. In suitable conditions, these mathematical equations can be simplified substantially to save computing time. The developed technologies of spectrum analysis take FFT to deal with the time-frequency transform work extensively. However, the sample of discrete signal is at random, and FFT suffers specific restrictions. When FFT transforms signal into frequency domain, the signal will cause errors on spectrum inevitably. This thesis corrects the errors by the optimization method. When frequency scales can match with signal characteristics, the picket-fence effect and leakage effect that the signal caused on spectrum will decrease to minimum. This method consists of three new technologies: parameter estimation, selection for optimal scale parameters, and adjustable spectrum. The method not only displays signal parameters on spectrum exactly and clearly, but also keeps the ability of fast process. When analyzing the more complex signal, the result of optimization will be restricted. Under this condition, the method can focus on the partial components and analyze them, then the result will keep accurate. This thesis combines supervisory technologies via a signal measurement. The signal sampling of these technologies is more convenient and simple. The system monitors operating conditions and fault conditions of the electric machinery with sound signal analysis. This signal analysis not only keeps normal measurement in the place which other signals can¡¦t be detected, but also can expand the monitoring ability. In operation conditions, the system monitors the speed and the input power of electric machinery through sound signal analysis. In fault conditions, the system recognizes type of fault under variation loads successfully. The recognition system is established by artificial neural network. The improvement of recognition ability is also discussed in this thesis. The methods discussed in the thesis give powerful estimation method for the signal analysis accurately and practically.

published_or_final_version / Physics / Master / Master of Philosophy

Thesis (Ph. D.)--Virginia Polytechnic Institute, 1963. / Vita. Abstract. Includes bibliographical references (leaves 124-126). Also available via the Internet.

Thesis (Ph.D.)--University of Rhode Island, 2005. / Includes bibliographical references (leaves 90-95).

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 115-117).

Current environmental and economic trends have forced grid operators to maximize the utilization of the existing assets, which is causing systems to be operated closer to their stability limits than ever before. This requires, among other things, better knowledge and modelling of the existing power system equipment to increase the accuracy of the assessment of current stability margins.This research investigates the possibility of improving the quality of load modeling. The thesis presents a review of the traditional methods for estimation of load model parameters and proposes to use Improved Particle Swarm Optimization. Different algorithms are tested and compared in terms of accuracy, reliability and CPU requirements using computer simulations and real-data captured in a power system.Estimation of frequency and power components has also been studied in this thesis. A review of the existing methods has been provided and the use of an Unscented Kalman Filter proposed. This nonlinear recursive algorithm has been thoroughly tested and compared against selected traditional techniques in a number of experiments involving computer-generated signals as well as measurements obtained in laboratory conditions.

Biological systems, processes, and applications present modeling challenges in the form of system complexity, limited steady-state availability, and limited measurements. One primary issue is the lack of well-estimated parameters. This thesis presents two contributions in the area of modeling and parameter estimation for these kinds of biological processes. The primary contribution is the development of an adaptive parameter estimation process that includes parameter selection, evaluation, and estimation, applied along with modeling of cell growth in culture. The second contribution shows the importance of parameter estimation for evaluation of experiment and process design. / Thesis / Master of Applied Science (MASc)