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This thesis represents an attempt to generalize the classical Theory of Optimal Design to popular regression models, based on Rational and Spline approximations. The problem of finding optimal designs for such models can be reduced to solving certain minimax problems. Explicit solutions to such problems can be obtained only in a few selected models, such as polynomial regression. Even when an optimal design can be found, it has, from the point of view of modern nonparametric regression, certain drawbacks. For example, in the polynomial regression case, the optimal design crucially depends on the degree m of approximating polynomial. Hence, it can be used only when such degree is given/known in advance. We present a partial, but practical, solution to this problem. Namely, the so-called Super Chebyshev Design has been found, which does not depend on the degree m of the underlying polynomial regression in a large range of m, and at the same time is asymptotically more than 90% efficient. Similar results are obtained in the case of rational regression, even though the exact form of optimal design in this case remains unknown. Optimal Designs in the case of Spline Interpolation are also currently unknown. This problem, however, has a simple solution in the case of Cardinal Spline Interpolation. Until recently, this model has been practically unknown in modern nonparametric regression. We demonstrate the usefulness of Cardinal Kernel Spline Estimates in nonparametric regression, by proving their asymptotic optimality, in certain classes of smooth functions. In this way, we have found, for the first time, a theoretical justification of a well known empirical observation, by which cubic splines suffice, in most practical applications. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2007-07-18 16:06:06.767

Performance regression refers to the phenomena where the application performance degrades compared to prior releases. Performance regressions are unwanted side-effects caused by changes to application or its execution environment. Previous research shows that most problems experienced by customers in the field are related to application performance. To reduce the likelihood of performance regressions slipping into production, software vendors must verify the performance of an application before its release. The current practice of performance verification is carried out only at the implementation level through performance tests. In a performance test, service requests with intensity similar to the production environment are pushed to the applications under test; various performance counters (e.g., CPU utilization) are recorded. Analysis of the results of performance verification is both time-consuming and error-prone due to the large volume of collected data, the absence of formal objectives and the subjectivity of performance analysts. Furthermore, since performance verification is done just before release, evaluation of high impact design changes is delayed until the end of the development lifecycle. In this thesis, we seek to improve the effectiveness of performance verification. First, we propose an approach to construct layered simulation models to support performance verification at the design level. Performance analysts can leverage our layered simulation models to evaluate the impact of a proposed design change before any development effort is committed. Second, we present an automated approach to detect performance regressions from results of performance tests conducted on the implementation of an application. Our approach compares the results of new tests against counter correlations extracted from performance testing repositories. Finally, we refine our automated analysis approach with ensemble-learning algorithms to evaluate performance tests conducted in heterogeneous software and hardware environments. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2011-01-31 15:53:02.732

Dietary flaxseed intake has exhibited both cardioprotective and anti-atherogenic properties. Regardless, it remains unclear whether these beneficial effects extent to the regression of atherosclerotic plaques or the resolution of cholesterol-induced vascular contractile dysfunction. In the present study, we intended to determine whether dietary flaxseed has the capacity to ameliorate vascular function abnormalities and induce atherosclerotic plaque regression. As results from previous studies using a nutritional intervention to induce atherosclerotic regression may have been confounded by premature initiation of the intervention, an appropriate feeding regimen was developed to adequately evaluate flaxseeds’ effects on atherosclerotic plaque regression. New Zealand white rabbits were utilized in two studies. To establish clear evidence of plaque growth stabilization, animals received 4 weeks of a 1% cholesterol-supplemented diet. An initial subset of animals was immediately examined. The remaining animals were fed regular rabbit chow and examined at intervals up to 28 weeks. To ascertain flaxseeds’ effects on atherosclerotic plaque regression and vascular contractile function, animals were randomly assigned to a control group fed a regular diet for 12 weeks (Group I) or an experimental group fed a 1% cholesterol-supplemented diet for 4 weeks followed by a regular diet for 8 weeks (Group II). The control and a subset of experimental animals were examined immediately afterwards. The remaining experimental animals were given an additional 8 or 14 weeks of either a regular diet (Group III and V, respectively) or a 10% flaxseed-supplemented diet (Group IV and VI, respectively) and were examined afterwards. Cholesterol feeding followed by 8 weeks of withdrawal from cholesterol not only resulted in the development and stabilization of atherosclerotic plaques but also impaired the maximum contraction caused by norepinephrine and the relaxation response to acetylcholine. An additional 14 weeks of regular diet reduced the amount of plaques on the aorta while flax-supplementation resulted in a further reduction in plaques. Nevertheless, both treatments were unable to achieve statistical significance. Flax- supplemented and regular diets improved vessel relaxation and contraction; however, negligible changes in the relaxation response induced by sodium nitroprusside were observed. Dietary flaxseed may accelerate the regression of atherosclerotic plaques. Moreover, the known beneficial effects of flaxseed do not extend to restoration of vascular function.

Climatic change has been observed in many locations and has been seen to have dramatic impact on a wide range of ecosystems. The traditional method to analyse trends in climatic series is regression analysis. Koenker and Bassett (1978) developed a regression-type model for estimating the functional relationship between predictor variables and any quantile in the distribution of the response variable. Quantile regression has received considerable attention in the statistical literature, but less so in the water resources literature. This study aims to apply quantile regression to problems in water resources and climate change studies. The core of the thesis is made up of three papers of which two have been published and one has been submitted. One paper presents a novel application of quantile regression to analyze the distribution of sea ice extent. Another paper investigates changes in temperature and precipitation extremes over the Canadian Prairies using quantile regression. The third paper presents a Bayesian model averaging method for variable selection adapted to quantile regression and analyzes the relationship of extreme precipitation with large-scale atmospheric variables. This last paper also develops a novel statistical downscaling model based on quantile regression. The various applications of quantile regression support the conclusion that the method is useful in climate change studies.

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