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

Most of the research was sponsored by the U.S. Geological Survey.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 124-131).

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.

Initial investigations of the Outlier Processing Method (OPM), first introduced by Birch [1][2][3] in 1988, have demonstrated a promising ability to extract a special class of signals, called highly variable events (HVEs), from coloured noise processes. The term HVE is introduced in this thesis to identify a finite-duration signal whose shape and latency vary dramatically from trial to trial and typically has a very low signal-to-noise ratio (SNR). This thesis presents a modified version of the original OPM algorithm, which can generate an estimate of the HVE with significantly less estimation noise than the original OPM algorithm. Simulation experiments are used to identify the strengths and limitations of this modified OPM algorithm for linear and stationary processes and to compare the modified algorithm's performance to the performance of the original algorithm and to the performance of a minimum mean-square-error (MMSE) filter. The results of these experiments verify that the modified algorithm can extract an HVE with less estimation noise than the original algorithm. The results also show, that the MMSE filter is unsuitable for extracting HVEs and that its performance is generally inferior to the modified algorithm's performance. The experiments indicate that the modified algorithm can extract HVEs from a linear and stationary process for SNR levels above -2.5dB and can work effectively above -7.5dB for HVEs with certain characteristics. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis describes a novel approach to model and estimate systems of unknown delay. The a-priori knowledge available about the systems is fully utilized so that the number of parameters to be estimated equals the number of unknowns in the systems. Existing methods represent the single unknown system delay by a large number of unknown parameters in the system model. The purpose of this thesis is to develop new methods of modelling the systems so that the unknowns are directly estimated. The Variable Regression Estimation technique is developed to provide direct delay estimation. The delay estimation requires minimum excitation and is robust, bounded, and it converges to the true value for first-order and second-order systems. The delay estimation provides a good model approximation for high-order systems and the model is always stable and matches the frequency response of the system at any given frequency. The new delay estimation method is coupled with the Pole Placement, Dahlin and the Generalized Predictive Controller (GPC) design and adaptive versions of these controllers result. The new adaptive GPC has the same closed-loop performance for different values of system delay. This was not achievable in the original adaptive GPC. The adaptive controllers with direct delay estimation can regulate systems with dominant time delay with minimum parameters in the controller and the system model. The delay does not lose identifiability in closed-loop estimation. Experiments on the delay estimation show excellent agreement with the theoretical analysis of the proposed methods. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis is concerned with the theory of fitting models of the form y = Xβ + ε, where some distributional assumptions are made on ε. More specifically, suppose that y[sub=j] = Zβ[sub=j] + ε [sub=j] is a model for a component j (j = 1, 2, ..., k) and that one is interested in estimation and interference theory relating to y[sub=T] = Σ [sup=k; sub=j=1] y[sub=j] = Xβ[sub=T] + ε[sub=T]. The theory of estimation and inference relating to the fitting of y[sub=T] is considered within the general framework of general linear model theory. The consequence of independence and dependence of the y[sub=j] (j = 1, 2, ..., k) for estimation and inference is investigated. It is shown that under the assumption of independence of the y[sub=j], the parameter vector of the total equation can easily be obtained by adding corresponding components of the estimates for the parameters of the component models. Under dependence, however, this additivity property seems to break down. Inference theory under dependence is much less tractable than under independence and depends critically, of course, upon whether y[sub=T] is normal or not. Finally, the theory of additivity is extended to classificatory models encountered in designed experiments. It is shown, however, that additivity does not hold in general in nonlinear models. The problem of additivity does not require new computing subroutines for estimation and inference in general in those cases where it works. / Forestry, Faculty of / Graduate

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In this thesis, two different topics are treated related to wireless communication. Part I presents three different reconfigurable MEMS integrated antennas for MIMO applications. Simulation and measurement results are presented along with brief discussions on the topic of antenna selection with reconfigurable antenna elements. Part II presents an estimator for the coupling matrix of an antenna array with two slightly different approaches. CRB is derived and discussed in terms of parameter cost. / <p>QC 20101119</p>