Singularly perturbed problems often yield solutions ith strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element meshes. The estimator is based on the solution of a local problem, and yields error bounds uniformly in the small perturbation parameter. The error estimation is efficient, i.e. a lower error bound holds. The error estimator is also reliable, i.e. an upper error bound holds, provided that the anisotropic mesh discretizes the problem sufficiently well. A numerical example supports the analysis of our anisotropic error estimator.

A singularly perturbed reaction-diffusion model problem is considered, and the choice of an appropriate norm is discussed. Particular emphasis is given to the energy norm. Certain prejudices against this norm are investigated and disproved. Moreover, an adaptive finite element algorithm is presented which exhibits an optimal error decrease in the energy norm in some simple numerical experiments. This underlines the suitability of the energy norm.

A singularly perturbed convection-diffusion problem in two and three space dimensions is discretized using the streamline upwind Petrov Galerkin (SUPG) variant of the finite element method. The dominant convection frequently gives rise to solutions with layers; hence anisotropic finite elements can be applied advantageously. The main focus is on a posteriori energy norm error estimation that is robust in the perturbation parameter and with respect to the mesh anisotropy. A residual error estimator and a local problem error estimator are proposed and investigated. The analysis reveals that the upper error bound depends on the alignment of the anisotropies of the mesh and of the solution. Hence reliable error estimation is possible for suitable anisotropic meshes. The lower error bound depends on the problem data via a local mesh Peclet number. Thus efficient error estimation is achieved for small mesh Peclet numbers. Altogether, error estimation approaches for isotropic meshes are successfully extended to anisotropic elements. Several numerical experiments support the analysis.

Disertacijoje nagrinemos problemos, iškylancios ieškant geriausios mažų sričių vertinimo strategijos. Ieškant geriausios mažų sričių vertinimo strategijos susiduriama su modelio parinkimo, imties plano ir ivertinio konstravimo, neatsakymu vertinimo ir papildomos informacijos panaudojimo problemomis. / In the dissertation special problems that may be encountered in finding optimal estimation strategy for small area estimation, in particular, model diagnostics for small area models, constrained estimation, sample design selection, nonresponse adjustment and borrowing strength across both small areas and time are considered.

This dissertation considers quantile regression models with nonstationary or nearly nonstationary time series. The first chapter outlines the thesis and discusses its theoretical and empirical contributions. The second chapter studies inference in quantile regressions with cointegrated variables allowing for multiple structural changes. The unknown break dates and regression coefficients are estimated jointly and consistently. The conditional quantile estimator has a nonstandard limit distribution. A fully modified estimator is proposed to remove the second-order bias and nuisance parameters and the resulting limit distribution is mixed normal. A simulation study shows that the fully modified quantile estimator has good finite sample properties. The model is applied to stock index data from the emerging markets of China and several mature markets. Financial market integration is found in some quantiles of the Chinese stock indices. The third chapter considers predictive quantile regression with a nearly integrated regressor. We derive nonstandard distributions for the quantile regression estimator and t-statistic in terms of functionals of diffusion processes. The critical values are found to depend on both the quantile of interest and the local-to-unity parameter, which is not consistently estimable. Based on these critical values, we propose a valid Bonferroni bounds test for quantile predictability with persistent regressors. We employ this new methodology to test the ability of many commonly employed and highly persistent regressors, such as the dividend yield, earnings price ratio, and T-bill rate, to predict the median, shoulders, and tails of the stock return distribution. Chapter Four proposes a cumulated sum (CUSUM) test for the null hypothesis of quantile cointegration. A fully modified quantile estimator is adopted for serial correlation and endogeneity corrections. The CUSUM statistic is composed of the partial sums of the residuals from the fully modified quantile regression. Under the null, the test statistic converges to a functional of Brownian motions. In the application to U.S. interest rates of different maturities, evidence in favor of the expectations hypothesis for the term structure is found in the central part of the distributions of the Treasury bill rate and financial commercial paper rate, but in the tails of the constant maturity rate distribution. / Thesis (Ph.D, Economics) -- Queen's University, 2012-07-30 15:20:38.253

This paper studies the use of Monte Carlo simulation techniques in the field of econometrics, specifically statistical inference. First, I examine several estimators by deriving properties explicitly and generate their distributions through simulations. Here, simulations are used to illustrate and support the analytical results. Then, I look at test statistics where derivations are costly because of the sensitivity of their critical values to the data generating processes. Simulations here establish significance and necessity for drawing statistical inference. Overall, the paper examines when and how simulations are needed in studying econometric theories.

We review several nonparametric regression techniques and discuss their various strengths and weaknesses with an emphasis on derivative estimation and confidence band creation. We develop a generalized C(p) criterion for tuning parameter selection when interest lies in estimating one or more derivatives and the estimator is both linear in the observed responses and self-consistent. We propose a method for constructing simultaneous confidence bands for the mean response and one or more derivatives, where simultaneous now refers both to values of the covariate and to all derivatives under consideration. In addition we generalize the simultaneous confidence bands to account for heteroscedastic noise. Finally, we consider the characterization of nanoparticles and propose a method for identifying a proper subset of the covariate space that is most useful for characterization purposes.

Power outages usually lead to customer complaints and revenue losses. Consequently, fast and accurate fault location on electric lines is needed so that repair work can be carried out as fast as possible. Chapter 2 describes novel fault location algorithms for radial and non-radial ungrounded power distribution systems. For both types of systems, fault location approaches using line to neutral or line to line measurements are presented. It’s assumed that network structure and parameters are known, so that during-fault bus impedance matrix of the system can be derived. Functions of bus impedance matrix and available measurements at substation are formulated, from which the unknown fault location can be estimated. Evaluation studies on fault location accuracy and robustness of fault location methods to load variations and measurement errors has been performed. Most existing fault location methods rely on measurements obtained from meters installed in power systems. To get the most from a limited number of meters available, optimal meter placement methods are needed. Chapter 3 presents a novel optimal meter placement algorithm to keep the system observable in terms of fault location determination. The observability of a fault location in power systems is defined first. Then, fault location observability analysis of the whole system is performed to determine the least number of meters needed and their best locations to achieve fault location observability. Case studies on fault location observability with limited meters are presented. Optimal meter deployment results based on the studied system with equal and varying monitoring cost for meters are displayed. To enhance fault location accuracy, an optimal fault location estimator for power distribution systems with distributed generation (DG) is described in Chapter 4. Voltages and currents at locations with power generation are adopted to give the best estimation of variables including measurements, fault location and fault resistances. Chi-square test is employed to detect and identify bad measurement. Evaluation studies are carried out to validate the effectiveness of optimal fault location estimator. A set of measurements with one bad measurement is utilized to test if a bad data can be identified successfully by the presented method.

This thesis concerns inference problems in balanced random effects models with a so-called block circular Toeplitz covariance structure. This class of covariance structures describes the dependency of some specific multivariate two-level data when both compound symmetry and circular symmetry appear simultaneously. We derive two covariance structures under two different invariance restrictions. The obtained covariance structures reflect both circularity and exchangeability present in the data. In particular, estimation in the balanced random effects with block circular covariance matrices is considered. The spectral properties of such patterned covariance matrices are provided. Maximum likelihood estimation is performed through the spectral decomposition of the patterned covariance matrices. Existence of the explicit maximum likelihood estimators is discussed and sufficient conditions for obtaining explicit and unique estimators for the variance-covariance components are derived. Different restricted models are discussed and the corresponding maximum likelihood estimators are presented. This thesis also deals with hypothesis testing of block covariance structures, especially block circular Toeplitz covariance matrices. We consider both so-called external tests and internal tests. In the external tests, various hypotheses about testing block covariance structures, as well as mean structures, are considered, and the internal tests are concerned with testing specific covariance parameters given the block circular Toeplitz structure. Likelihood ratio tests are constructed, and the null distributions of the corresponding test statistics are derived.

Exhaustible resource rents are an important taxable base in many countries, with revenue sharing often part of the scheme. In some cases large shares are retained for the central government. Generally, the discussions of exhaustible resource taxation consider assignment of resource rent tax base and revenue sharing from the limited perspectives of efficiency and stability. Tax assignment and sharing arrangements are assumed to have a neutral effect on investment of resource rents in long-lived public goods. We attempt to demonstrate that this may not be the case, specifically looking at the question of whether rent assignment is neutral to effects on investment of rents in long-lived public goods, a normative policy objective, and under what conditions it occurs. We test the theoretical propositions with data from the Russian Federation to derive empirical results. The results from the Russian Federation point toward an important dimension of rent tax assignment in a federation. They results show that ceteris paribus, higher share of rent for the federation may lead to lower investment in long-lived public goods and may be constrained by stability. Another argument has been made for reconsidering rent tax assignment using assertive ethnic identity as a manifestation strong ownership claims. Communities with strongly valued identities value ownership over land and exhaustible resource endowments in their areas. This may be the case especially if ethnic identity is important to the resource owning community. The empirical results show that a decrease in the regional share of rent resulted in a fall in investments in the republics and regions with strong ethnic identity. Republics among the producing regions have historical claims to a distinct identity and may have a preference for preserving their identity. This preference is manifested as higher levels of rent investment. Following this line of argument, it can be concluded that rent assignment, through rent tax or revenue assignment, should favor producing regions within the range of stability in a federation, if the objective is achieving higher investment in long-lived public goods.