<p>Techniques for a posteriori error estimation for finite element approximations of an elliptic partial differential equation are studied.This extends previous work on localized error control in finite element methods for linear elasticity.The methods are then applied to the problem of homogenization of periodic structures. In particular, error estimates for the effective elastic properties are obtained. The usefulness of these estimates is twofold.First, adaptive methods using mesh refinements based on the estimates can be constructed.Secondly, one of the estimates can give reasonable measure of the magnitude ofthe error. Numerical examples of this are given.</p>

This dissertation is composed of three essays regarding the finite sample properties of estimators for nonparametric models. In the first essay we investigate the finite sample performances of four estimators for additive nonparametric regression models - the backfitting B-estimator, the marginal integration M-estimator and two versions of a two stage 2S-estimator, the first proposed by Kim, Linton and Hengartner (1999) and the second which we propose in this essay. We derive the conditional bias and variance of the 2S estimators and suggest a procedure to obtain optimal bandwidths that minimize an asymptotic approximation of the mean average squared errors (AMASE). We are particularly concerned with the performance of these estimators when bandwidth selection is done based on data driven methods. We compare the estimators' performances based on various bandwidth selection procedures that are currently available in the literature as well as with the procedures proposed herein via a Monte Carlo study. The second essay is concerned with some recently proposed kernel estimators for panel data models. These estimators include the local linear estimator, the quasi-likelihood estimator, the pre-whitening estimators, and the marginal kernel estimator. We focus on the finite sample properties of the above mentioned estimators on random effects panel data models with different within-subject correlation structures. For each estimator, we use the asymptotic mean average squared errors (AMASE) as the criterion function to select the bandwidth. The relative performance of the test estimators are compared based on their average squared errors, average biases and variances. The third essay is concerned with the finite sample properties of estimators for nonparametric regression models with autoregressive errors. The estimators studied are: the local linear, the quasi-likelihood, and two pre-whitening estimators. Bandwidths are selected based on the minimization of the asymptotic mean average squared errors (AMASE) for each estimator. Two regression functions and multiple variants of autoregressive processes are employed in the simulation. Comparison of the relative performances is based mainly on the estimators' average squared errors (ASE). Our ultimate objective is to provide an extensive finite sample comparison among competing estimators with a practically selected bandwidth. / Graduation date: 2006

We present a novel approach to parameter estimation of systems with complicated dynamics, as well as evidence for the existence of a universal power law that enables us to quantify the dependence of global geometry on small changes in the parameters of the system. This power law gives rise to what seems to be a new dynamical system invariant.

In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Procedure (MLE) and the greedy procedure described by Li and Barron. Approximation and estimation bounds are given for the above methods. We extend and improve upon the estimation results of Li and Barron, and in particular prove an $O(\\frac{1}{\\sqrt{n}})$ bound on the estimation error which does not depend on the number of densities in the estimated combination.

Given a set of images from the same viewpoint, in which occlusions are present, background estimation is to output an image with stationary objects in the scene only. Background estimation is an important step in many computer vision problems such as object detection and recognition. With the growing interest in more sophisticated video surveillance systems, the requirement for the accuracy of background estimation increases as well. In this thesis, we present two novel methods whose fundamental objectives are the same, namely, to estimate the background of a set of related images. In order to make our methods more general, we assume that the input images can be taken either from the same viewpoint or from different viewpoints. Both methods combine information from multiple input images by selecting the appropriate pixels to construct the background. Our first method is a scanline energy optimization method, and our second method is based on graph cuts optimization. We apply these two methods to datasets with different feature and the results are encouraging. Furthermore, we use the CUDA (Compute Unified Device Architecture) programming language to make full use of the GPU processing power. GPU stands for Graphics Processing Unit, which employs parallel processing and is more powerful than the CPU. In particular, we implement an efficient graph-based image segmentation algorithm as well as a linear blending method using the CUDA programming language for acceleration, both of which are used in our first method. The speedup of our GPU implementation can be 20 times faster.

Orthogonal frequency-division multiplexing (OFDM) has been employed in several current and future 4-th generation (4G) wireless standards. Frequency offsets in OFDM introduce intercarrier interference (ICI). Channel estimations are also required. This thesis focuses on the channel and frequency offset estimation for OFDM-based systems. For cooperative-relay OFDM with frequency offsets, where inter-relay interference (IRI) exists, channel estimation is developed. Optimal pilot designs are proposed by minimizing the IRI in the mean square error (MSE) of the least square (LS) channel estimation. The impact of frequency offset on the channel estimation accuracy is derived. The pairwise error probability (PEP) with both the frequency offset and channel estimation errors is evaluated. The power allocation is discussed. For multiple-input multiple-output (MIMO) OFDM systems, channel and frequency offset estimation errors are investigated. The signal-to-interference-and-noise ratio (SINR) is first analyzed given channel and frequency offset estimation errors. The bit error rate (BER) is then approximated for multiple-antenna reception with maximal ratio combing (MRC) and equal gain combining (EGC). For orthogonal frequency-division multiplexing access (OFDMA) systems, the variance of the frequency offset estimation is derived as a function of SINR and signal-to- noise ratio (SNR). This variance information is exploited to improve the accuracy of frequency offset estimators. A successive interference cancellation (SIC)-based frequency offset estimator is also developed. The accuracy of frequency offset estimation of the OFDMA uplink can also be improved by using the cooperative relaying. Both conventional amplify-and-forward (AF) relays and new decode-and-compensate-and-forward (DcF) relays are studied. The frequency offset estimate is derived from combining different link estimates. In addition, when CSI is available, a scheme is proposed to adaptively switch between the cooperative and conventional (no relaying) transmissions to optimize the frequency offset estimation. / Wireless Communications

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (M. P. A.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

In this thesis, a novel training sequence is proposed for timing offset estimation in orthogonal frequency division multiplexing (OFDM) systems. The proposed training sequence and the derived timing offset estimator are proved to outperform traditional schemes. In timing estimation of OFDM systems, the scheme proposed by Schmidl [4,5] is perhaps the most well-known one. However, Schmidl¡¦s scheme has a plateau in timing metric, which substantially degrades system performance. In this thesis, simulation experiments are conducted to evaluate the performance of the proposed timing offset estimator and the mean square error (MSE) is adopted as the performance measure. Simulation results demonstrate that the performance of the proposed scheme not only improves Schmidl¡¦s scheme, but also outperforms Minn¡¦s [9] and Park¡¦s [10] schemes.

In this thesis, we investigate and implement the channel estimation schemes for digital video broadcasting - handheld (DVB-H) and IEEE 802.16d world interoperability for micro-wave access (WiMAX). Both systems are based on the orthogonal frequency division multiplexing (OFDM) technique. The performance of the channel estimation schemes is first verified by using simulation experiments. Then, the channel estimation algorithms are realized by hardware implementation. For the DVB-H systems, since the mobile device may have a relatively high speed, the channel condition is time-varying, leading to serious degradation in channel estimation. In this thesis, the decision feedback mechanism is adopted to improve the performance of the channel estimation. The adopted structure for channel estimation is realized by using Verilog hardware description language (HDL). Then, all the baseband signal processing related algorithms, which include timing synchronization, frequency offset estimation/compensation, and scattered pilot detection, are integrated together using 0.18 ASIC process. For the IEEE 802.16d WiMAX, since it is dedicated for fixed wireless applications, the channel condition is basically stationary and easier to obtain. Therefore, the decision feedback mechanism is not adopted to save hardware complexity. The system performance is verified by conducting simulation experiments. The adopted channel estimation algorithm is implemented by using Verilog HDL. Finally, the whole baseband receiver is realized by using the field programmable gate array (FPGA) and verified by using the Agilent logic analyzer.