The second-order least-squares estimator (SLSE), which was proposed by Wang (2003), is asymptotically more efficient than the least-squares estimator (LSE) if the third moment of the error distribution is nonzero. However, it is not robust against outliers. In this paper. we propose two robust second-order least-squares estimators (RSLSE) for linear regression models. RSLSE-I and RSLSE-II, where RSLSE-I is robust against X-outliers and RSLSE-II is robust. against X-outliers and Y-outliers. The basic idea is to choose proper weight matrices, which give a zero weight to an outlier. The RSLSEs are asymptotically normally distributed and are highly efficient with high breakdown point.. Moreover, we compare the RSLSEs with the LSE, the SLSE and the robust MM-estimator through simulation studies and real data examples. The results show that they perform very well and are competitive to other robust regression estimators.

Least squares linear regression is a common tool in ecological research. One of the central assumptions of least squares linear regression is that the independent variable is measured without error. But this variable is measured with error whenever it is a sample mean. The significance of such contraventions is not regularly assessed in ecological studies. A simulation program was made to provide such an assessment. The program requires a hypothetical data set, and using estimates of S$ sp2$ it scatters the hypothetical data to simulate the effect of sampling error. A regression line is drawn through the scattered data, and SSE and r$ sp2$ are measured. This is repeated numerous times (e.g. 1000) to generate probability distributions for r$ sp2$ and SSE. From these distributions it is possible to assess the likelihood of the hypothetical data resulting in a given SSE or r$ sp2$. The method was applied to survey data used in a published TP-CHLa regression (Pace 1984). Beginning with a hypothetical, linear data set (r$ sp2$ = 1), simulated scatter due to sampling exceeded the SSE from the regression through the survey data about 30% of the time. Thus chances are 3 out of 10 that the level of uncertainty found in the surveyed TP-CHLa relationship would be observed if the true relationship were perfectly linear. If this is so, more precise and more comprehensive models will only be possible when better estimates of the means are available. This simulation approach should apply to all least squares regression studies that use sampled means, and should be especially relevant to studies that use log-transformed values.

Modern power networks are being driven ever closer to both their physical and operational limits. As a result, control systems are being increasingly relied on to assure satisfactory system performance. Power system stabilizers (PSSs) are one example of such controllers. Their purpose is to increase system damping and they are typically designed using a model of the network that is valid during nominal operating conditions. The limitation of this design approach is that during off-nominal operating conditions, such as those triggered by daily load fluctuations, performance of the controller can degrade. The research presented in this report attempts to evaluate the possibility of employing an adaptive PSS as a means of avoiding the performance degradation precipitated by off-nominal operation. Conceptually, an adaptive PSS would be capable of identifying changes in the network and then adjusting its parameters to ensure suitable damping of the identified network. This work begins with a detailed look at the identification algorithm employed followed by a similarly detailed examination of the control algorithm that was used. The results of these two investigations are then combined to allow for a preliminary assessment of the performance that could be expected from an adaptive PSS. The results of this research suggest that an adaptive PSS is a possibility but further work is needed to confirm this finding. Testing using more complex network models must be carried out, details pertaining to control parameter tuning must be resolved and closed-loop time domain simulations using the adaptive PSS design remain to be performed.

Variable digital filters (VDF) find many application areas in communication, audio, speech and image processing. This thesis analyzes design and implementation of FIR digital filters with variable frequency characteristics and introduces two design methods. The design and implementation of the proposed methods are realized on Matlab software program. Various filter design examples and comparisons are also outlilned. One of the major application areas of VDFs is software defined radio (SDR). The interpolation problem on sample rate converter (SRC) unit of the SDR is solved by using these filters. Realizations of VDFs on SRC are outlined and described. Simulations on Simulink and a specific hardware are examined.

We study the consistency, robustness and efficiency of parameter estimation in different but related models via semiparametric approach. First, we revisit the second- order least squares estimator proposed in Wang and Leblanc (2008) and show that the estimator reaches the semiparametric efficiency. We further extend the method to the heteroscedastic error models and propose a semiparametric efficient estimator in this more general setting. Second, we study a class of semiparametric skewed distributions arising when the sample selection process causes sampling bias for the observations. We begin by assuming the anti-symmetric property to the skewing function. Taking into account the symmetric nature of the population distribution, we propose consistent estimators for the center of the symmetric population. These estimators are robust to model misspecification and reach the minimum possible estimation variance. Next, we extend the model to permit a more flexible skewing structure. Without assuming a particular form of the skewing function, we propose both consistent and efficient estimators for the center of the symmetric population using a semiparametric method. We also analyze the asymptotic properties and derive the corresponding inference procedures. Numerical results are provided to support the results and illustrate the finite sample performance of the proposed estimators.

Geodesy deals with the accurate analysis of spatial and temporal variations in the geometry and physics of the Earth at local and global scales. In geodesy, least-squares collocation (LSC) is a bridge between the physical and statistical understanding of different functionals of the gravitational field of the Earth. This thesis specifically focuses on the [incorrect] implicit LSC assumptions of isotropy and homogeneity that create limitations on the application of LSC in non-stationary gravity field modeling. In particular, the work seeks to derive expressions for local and global analytical covariance functions that account for the anisotropy and heterogeneity of the Earth's gravity field. / Standard LSC assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing, e.g., of the gravity field in mountains and under-smoothing in great plains. The kernel convolution method from spatial statistics is introduced for non-stationary covariance structures, and its advantage in dealing with non-stationarity in geodetic data is demonstrated. / Tests of the new non-stationary solutions were performed over the Darling Fault, Western Australia, where the anomalous gravity field is anisotropic and non-stationary. Stationary and non-stationary covariance functions are compared in 2D LSC to the empirical example of gravity anomaly interpolation. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation. Both non-stationarity of mean and covariance are considered in planar geoid determination by LSC to test how differently non-stationarity of mean and covariance affects the LSC result compared with GPS-levelling points in this area. Non-stationarity of the mean was not very considerable in this case, but non-stationary covariances were very effective when optimising the gravimetric quasigeoid to agree with the geometric quasigeoid. / In addition, the importance of the choice of the parameters of the non-stationary covariance functions within a Bayesian framework and the improvement of the new method for different functionals on the globe are pointed out.

As the spatial information industry moves from an era of data collection to one of data maintenance, new integration methods to consolidate or to update datasets are required. These must reduce the discrepancies that are becoming increasingly apparent when spatial datasets are overlaid. It is essential that any such methods consider the quality characteristics of, firstly, the data being integrated and, secondly, the resultant data. This thesis develops techniques that give due consideration to data quality during the integration process.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 213-219).

Thesis (M.S.)--Florida State University, 2004. / Advisor: Dr. Simon Y. Foo, Florida State University, College of Engineering, Dept. of Electrical and Computer Engineering. Title and description from dissertation home page (viewed Sept. 27, 2004). Includes bibliographical references.

Thesis (M.S.)--Indiana University, 2008. / Title from screen (viewed on June 3, 2009). Department of Earth Science, Indiana University-Purdue University Indianapolis (IUPUI). Advisor(s): Lin Li, Pierre Jacinthe, Gabriel M. Filippelli. Includes vita. Includes bibliographical references (leaves 78-81).