Nonparametric procedures use weak assumptions such as continuity of the distribution so that they are applicable to a large class F of underlying distributions. Statistics that are distribution-free over F may be constructed to be estimators of location. Such estimators are derived from rank tests called R-estimators. They are robust estimators. The concept of robust estimation is based on a neighborhood of parametric models called "gross error models". The M-estimator, which is a maximum likelihood type estimator, arose from such investigations using the normal distribution. A third big class of estimators is the class of linear combinations of order statistics called L-estimators. They are constructed as an average of quantiles. Examples are the sample mean and the sample median.In this thesis, some definitions and results involving these three basic classes of estimates are provided. For each class, an example of a robust estimator is presented. Numerical values are given to assess the robustness of each estimator in terms of breakdown point and gross error sensitivity. Further, the U-statistics which are unbiased estimators of location parameters, are used to obtain asymptotically efficient R-estimates. / Department of Mathematical Sciences

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 164-168). Also available via the Internet.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 215-226). Also available via the Internet.

It has become obvious that combined arrays and a response surface approach can be effective tools in our quest to reduce (process) variability. An important aspect of the improvement of quality is to suppress the magnitude of the influence coming from subtle changes of noise factors. To model and control process variability induced by noise factors we take a response surface approach. The derivative of the standard response function with respect to noise factors, i. e., the slopes of the response function in the direction of the noise factors, play an important role in the study of the minimum process variance. For better understanding of the process variability, we study various properties of both biased and the unbiased estimators of the process variance. Response surface modeling techniques and the ideas involved with variance modeling and estimation through the function of the aforementioned derivatives is a valuable concept in this study. In what follows, we describe the use of the response surface methodology for situations in which noise factors are used. The approach is to combine Taguchi's notion of heterogeneous variability with standard design and modeling techniques available in response surface methodology. / Ph. D.

This thesis generalizes the concept of internal feedback loop modeling, due to Tahk and Speyer, to arrive at two new LQG-based methods of parameter robust control. One component of the robustness procedure, common to both methods, is the application of an auxiliary cost functional penalty to desensitize the system to variations in selected parameters of the state-space model. The other component consists of the formulation of a fictitious noise model to accommodate the effect of these parameter variations. The "frequency-domain method" utilizes knowledge of the system dynamics to create a frequency-shaped noise model with a power spectrum that approximates the frequency content of unknown error signals in the system due to parameter uncertainties. This design method requires augmentation of additional dynamics to the plant, which results in higher-dimensional full-order controllers. However, the controller design computations are identical to those of a standard LQG problem. The "time-domain method" emulates the same error signals by means of a multiplicative white noise model which reflects the time-domain behavior of those signals. The resulting robust controller is of the same order as the standard LQG controller, although the design involves a more complex computational algorithm. The application of multiplicative white noise to the system model requires the solution of a system of four coupled equations - two modified Riccati equations and two modified Lyapunov equations. In addition, the optimal projection equations are applied to both robustness methods to reduce the controller order with minimal loss in performance. Comparisons are drawn between these and related robust control methods, and it is shown that the relative effectiveness of such methods is problem dependent. Parameter sensitivity analysis is carried out on a simply supported plate model subject to external disturbances. The appropriate robust controller is selected, and it is found to stabilize the plate with little sacrifice in performance. / Ph. D.

This thesis presents a new robust filtering technique that suppresses impulsive noise in speech signals. The method makes use of Projection Statistics based on medians to detect segments of speech with impulses. The autoregressive model employed to smooth out the speech signal is identified by means of a robust nonlinear estimator known as the Schweppe-type Huber GM-estimator. Simulation results are presented that demonstrate the effectiveness of the filter. Another contribution of the work is the development of a robust version of the Kalman filter based on the Huber M-estimator. The performances of this filter are evaluated for a simple autoregressive process. / Master of Science

by Ho, Kei Shiu Edward. / "June 1996." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (p. 186-193). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web.

by David C. Hoaglin, Stephen C. Peters. / Bibliography: leaf [5] / Caption title. "May, 1979." / National Science Foundation Grant SOC75-15702 National Science Foundation Grant MCS77-26902 National Science Foundation Grant MCS78-17697

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

(Uncorrected OCR) Abstract Abstract of thesis entitled Robust Statistics Based Adaptive Filtering Algorithms For Impulsive Noise Suppression Submitted by Yuexian Zou for the degree of Doctor of Philosophy at The University of Hong Kong in May 2000 The behavior of an adaptive filter is inherently decided by how its estimation error and the cost function are formulated under certain assumption of the involving signal statistics. This dissertation is concerned with the development of robust adaptive filtering in an impulsive noise environment based on the linear transversal filter (LTF) and the lattice-ladder filer (LLF) structures. Combining the linear adaptive filtering theory and robust statistics estimation techniques, two new cost functions, called the mean M -estimate error (MME) and the sum of weighted M -estimate error (SWME), are proposed. They can be taken as the generalizations of the well-known mean squared error (MSE) and the sum of weighted squares error (SWSE) cost functions when the involving signals are Gaussian. Based on the SWME cost function, the resulting optimal weight vector is governed by an M-estimate normal equation and a recursive least M -estimate (RLM) algorithm is derived. The RLM algorithm preserves the fast initial convergence, lower steady-state 11 Abstract derived. The RLM algorithm preserves the fast initial convergence, lower steady-state error and the robustness to the sudden system change of the recursive least squares (RLS) algorithm under Gaussian noise alone. Meanwhile, it has the ability to suppress impulse noise both in the desired and input signals. In addition, using the MME cost function, stochastic gradient based adaptive algorithms, named the least mean Mestimate (LMM) and its transform dOlnain version, the transform domain least mean Mestimate (TLMM) algorithms have been developed. The LMM and TLMM algorithms can be taken as the generalizations of the least-mean square (LMS) and transform domain normalized LMS (TLMS) algorithms, respectively. These two robust algorithms give similar performance as the LMS and TLMS algorithms under Gaussian noise alone and are able to suppress impulse noise appearing in the desired and input signals. It is noted that the performance and the computational complexity of the RLM, LMM and TLMM algorithms have a close relationship with the estimate of the threshold parameters for the M-estimate functions. A robust and effective recursive method has been suggested in this dissertation to estimate the variance of the estimation error and the required threshold parameters with certain confidence to suppress the impulsive noise. The mean and mean square convergence performances of the RLM and the LMM algorithms are evaluated, respectively, when the impulse noise is assumed to be contaminated Gaussian distribution. Motivated by the desirable features of the lattice-ladder filter, a new robust adaptive gradient lattice-ladder filtering algorithm is developed by minimizing an MME cost function together with an embedded robust impulse suppressing process, especially for impulses appearing in the filter input. The resultant robust gradient lattice-robust 111 Abstract normalized LMS (RGAL-RNLMS) algorithm perfonns comparably to the conventional GAL-NLMS algorithm under Gaussian noise alone; meanwhile, it has the capability of suppressing the adverse effects due to impulses in the input and the desired signals. The additional computational complexity compared to the GAL-NLMS algorithm is of O(Nw log Nw) + O(NfI log N,J . Extensive computer simulation studies are undertaken to evaluate the performance of the RLM, LMM, TLMM and the RGAL-RNLMS algorithms under the additive noise with either a contaminated Gaussian distribution or the symmetric alpha-stable (SaS ) distributions. The results substantiate the analysis and demonstrate the effectiveness and robustness of the developed robust adaptive filtering algorithms in suppressing impulsive noise both in the input and the desired signals of the adaptive filter. In conclusion, the proposed approaches in this dissertation present an attempt for developing robust adaptive filtering algorithms in impulsive noise environments and can be viewed as an extension of the linear adaptive filter theory. They may become reasonable and effective tools to solve adaptive filtering problems in a non-Gaussian environment in practice. IV / abstract / toc / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy