In this study we develop a new method for testing the null hypothesis that the predictor function in a canonical link regression model has a prescribed linear form. The class of models, which we will refer to as canonical link regression models, constitutes arguably the most important subclass of generalized linear models and includes several of the most popular generalized linear models. In addition to the primary contribution of this study, we will revisit several other tests in the existing literature. The common feature among the proposed test, as well as the existing tests, is that they are all based on orthogonal series estimators and used to detect departures from a null model. Our proposal for a new lack-of-fit test is inspired by the recent contribution of Hart and is based on a Laplace approximation to the posterior probability of the null hypothesis. Despite having a Bayesian construction, the resulting statistic is implemented in a frequentist fashion. The formulation of the statistic is based on characterizing departures from the predictor function in terms of Fourier coefficients, and subsequent testing that all of these coefficients are 0. The resulting test statistic can be characterized as a weighted sum of exponentiated squared Fourier coefficient estimators, whereas the weights depend on user-specified prior probabilities. The prior probabilities provide the investigator the flexibility to examine specific departures from the prescribed model. Alternatively, the use of noninformative priors produces a new omnibus lack-of-fit statistic. We present a thorough numerical study of the proposed test and the various existing orthogonal series-based tests in the context of the logistic regression model. Simulation studies demonstrate that the test statistics under consideration possess desirable power properties against alternatives that have been identified in the existing literature as being important.

<p>This paper offers to measure efficiency of banks in Sub Saharan Africa and its determining input andout put factors on two fonts. At this purpose, we applied the first font; Data Envelopment Analysis(DEA) for assessing efficiency level. The actual and target level of inputs/outputs to foster efficiencyare shown in the results. Secondly, the banks ratio analysis measuring banks performance throughreturns volatility for each bank, asset utilization and provision for bad and doubtful debts over thestudy period are all used as tools for this analysis. Our results suggest that Sub Saharan AfricanBanks are about 98.35% efficient. We are aware that the level of efficiency could be subject to up anddown swing if environmental factors influencing banks efficiency where taken into consideration.Finally, our result (DEA) is more sensitive to loans, other liabilities, other non interest expense,securities and deposit.</p>

Thesis (M.S.)--University of North Carolina at Wilmington, 2003. / Includes bibliographical references (leaf : [101]).

Thesis (M.S.)--University of North Carolina at Wilmington, 2003. / Includes bibliographical references (leaf : [40]).

DNA microarrays have been used for the purpose of monitoring expression levels of thousands of genes simultaneously and identifying those genes that are differentially expressed. One of the major goals of microarray data analysis is the detection of differentially expressed genes across two kinds of tissue samples or samples obtained under two experimental conditions. A large number of gene detection methods have been developed and most of them are based on statistical analysis. However the statistical analysis methods have the limitations due to the small sample size and unknown distribution and error structure of microarray data. In this thesis, a study of ranking-based gene selection methods which have weak assumption about the data was done. Three approaches are proposed to integrate the individual ranks to select differentially expressed genes in microarray data. The experiments are implemented on the simulated and biological microarray data, and the results show that ranking-based methods outperform the t-test and SAM in selecting differentially expressed genes, especially when the sample size is small.

Traditionally radio spectrum was considered a commodity to be allocated in a fixed and centralized manner, but now the technical community and the regulators approach it as a shared resource that can be flexibly and intelligently shared between competing entities. In this thesis we focus on novel strategies to sense and access the radio spectrum within the framework of Opportunistic Spectrum Access via Cognitive Radio Networks (CRNs). In the first part we develop novel transmit opportunity detection methods that effectively exploit the gray space present in packet based networks. Our methods proactively detect the maximum safe transmit power that does not significantly affect the primary network nodes via an implicit feedback mechanism from the Primary network to the Secondary network. A novel use of packet interarrival duration is developed to robustly perform change detection in the primary network's Quality of Service. The methods are validated on real world IEEE 802.11 WLANs. In the second part we study the inferential use of Goodness-of-Fit tests for spectrum sensing applications. We provide the first comprehensive framework for decision fusion of an ensemble of goodness-of-fit tests through use of p-values. Also, we introduce a generalized Phi-divergence statistic to formulate goodness-of-fit tests that are tunable via a single parameter. We show that under uncertainty in the noise statistics or non-Gaussianity in the noise, the performance of such non-parametric tests is significantly superior to that of conventional spectrum sensing methods. Additionally, we describe a collaborative spatially separated version of the test for robust combining of tests in a distributed spectrum sensing setting. In the third part we develop the sequential energy detection problem for spectrum sensing and formulate a novel Sequential Energy Detector. Through extensive simulations we demonstrate that our doubly hierarchical sequential testing architecture delivers a significant throughput improvement of 2 to 6 times over the fixed sample size test while maintaining equivalent operating characteristics as measured by the Probabilities of Detection and False Alarm. We also demonstrate the throughput gains for a case study of sensing ATSC television signals in IEEE 802.22 systems. / text

A complex system is one with many parts, whose behaviors are strongly dependent on each other. There are two interesting questions about complex systems. One is to understand how to recover the true structure of a complex system from noisy data. The other is to understand how the system interacts with its environment. In this thesis, we address these two questions by studying two distinct complex systems: dynamic systems and market microstructure. To address the first question, we focus on some nonlinear dynamic systems. We develop a novel Bayesian statistical method, Gaussian Emulator, to estimate the parameters of dynamic systems from noisy data, when the data are either fully or partially observed. Our method shows that estimation accuracy is substantially improved and computation is faster, compared to the numerical solvers. To address the second question, we focus on the market microstructure of hidden liquidity. We propose some statistical models to explain the hidden liquidity under different market conditions. Our statistical results suggest that hidden liquidity can be reliably predicted given the visible state of the market. / Statistics

This thesis presents certain recent methodologies and some new results for the statistical analysis of probability distributions on non-Euclidean manifolds. The notions of Frechet mean and variation as measures of center and spread are introduced and their properties are discussed. The sample estimates from a random sample are shown to be consistent under fairly broad conditions. Depending on the choice of distance on the manifold, intrinsic and extrinsic statistical analyses are carried out. In both cases, sufficient conditions are derived for the uniqueness of the population means and for the asymptotic normality of the sample estimates. Analytic expressions for the parameters in the asymptotic distributions are derived. The manifolds of particular interest in this thesis are the shape spaces of k-ads. The statistical analysis tools developed on general manifolds are applied to the spaces of direct similarity shapes, planar shapes, reflection similarity shapes, affine shapes and projective shapes. Two-sample nonparametric tests are constructed to compare the mean shapes and variation in shapes for two random samples. The samples in consideration can be either independent of each other or be the outcome of a matched pair experiment. The testing procedures are based on the asymptotic distribution of the test statistics, or on nonparametric bootstrap methods suitably constructed. Real life examples are included to illustrate the theory.

This paper offers to measure efficiency of banks in Sub Saharan Africa and its determining input andout put factors on two fonts. At this purpose, we applied the first font; Data Envelopment Analysis(DEA) for assessing efficiency level. The actual and target level of inputs/outputs to foster efficiencyare shown in the results. Secondly, the banks ratio analysis measuring banks performance throughreturns volatility for each bank, asset utilization and provision for bad and doubtful debts over thestudy period are all used as tools for this analysis. Our results suggest that Sub Saharan AfricanBanks are about 98.35% efficient. We are aware that the level of efficiency could be subject to up anddown swing if environmental factors influencing banks efficiency where taken into consideration.Finally, our result (DEA) is more sensitive to loans, other liabilities, other non interest expense,securities and deposit.

<p>Capturing high dimensional complex ensembles of data is becoming commonplace in a variety of application areas. Some examples include</p><p>biological studies exploring relationships between genetic mutations and diseases, atmospheric and spatial data, and internet usage and online behavioral data. These large complex data present many challenges in their modeling and statistical analysis. Motivated by high dimensional data applications, in this thesis, we focus on building scalable Bayesian nonparametric regression algorithms and on developing models for joint distributions of complex object ensembles.</p><p>We begin with a scalable method for Gaussian process regression, a commonly used tool for nonparametric regression, prediction and spatial modeling. A very common bottleneck for large data sets is the need for repeated inversions of a big covariance matrix, which is required for likelihood evaluation and inference. Such inversion can be practically infeasible and even if implemented, highly numerically unstable. We propose an algorithm utilizing random projection ideas to construct flexible, computationally efficient and easy to implement approaches for generic scenarios. We then further improve the algorithm incorporating some structure and blocking ideas in our random projections and demonstrate their applicability in other contexts requiring inversion of large covariance matrices. We show theoretical guarantees for performance as well as substantial improvements over existing methods with simulated and real data. A by product of the work is that we discover hitherto unknown equivalences between approaches in machine learning, random linear algebra and Bayesian statistics. We finally connect random projection methods for large dimensional predictors and large sample size under a unifying theoretical framework.</p><p>The other focus of this thesis is joint modeling of complex ensembles of data from different domains. This goes beyond traditional relational modeling of ensembles of one type of data and relies on probability mixing measures over tensors. These models have added flexibility over some existing product mixture model approaches in letting each component of the ensemble have its own dependent cluster structure. We further investigate the question of measuring dependence between variables of different types and propose a very general novel scaled measure based on divergences between the joint and marginal distributions of the objects. Once again, we show excellent performance in both simulated and real data scenarios.</p> / Dissertation