Includes bibliographical references (p. 38-40).

This thesis consists of two topics: statistical selection and profile monitoring. Statistical selection is related to ranking and selection in simulation and profile monitoring is related to statistical process control. Ranking and selection (R&S) is to select a system with the largest or smallest performance measure among a finite number of simulated alternatives with some guarantee about correctness. Fully sequential procedures have been shown to be efficient, but their actual probabilities of correct selection tend to be higher than the nominal level, implying that they consume unnecessary observations. In the first part, we study three conservativeness sources in fully sequential indifference-zone (IZ) procedures and use experiments to quantify the impact of each source in terms of the number of observations, followed by an asymptotic analysis on the impact of the critical one. Then we propose new asymptotically valid procedures that lessen the critical conservativeness source, by mean update with or without variance update. Experimental results showed that new procedures achieved meaningful improvement on the efficiency. The second part is developing a wavelet-based distribution-free tabular CUSUM chart based on adaptive thresholding. WDFTCa is designed for rapidly detecting shifts in the mean of a high-dimensional profile whose noise components have a continuous nonsingular multivariate distribution. First computing a discrete wavelet transform of the noise vectors for randomly sampled Phase I (in-control) profiles, WDFTCa uses a matrix-regularization method to estimate the covariance matrix of the wavelet-transformed noise vectors; then those vectors are aggregated (batched) so that the nonoverlapping batch means of the wavelet-transformed noise vectors have manageable covariances. Lower and upper in-control thresholds are computed for the resulting batch means of the wavelet-transformed noise vectors using the associated marginal Cornish-Fisher expansions that have been suitably adjusted for between-component correlations. From the thresholded batch means of the wavelet-transformed noise vectors, Hotelling’s T^2-type statistics are computed to set the parameters of a CUSUM procedure. To monitor shifts in the mean profile during Phase II (regular) operation, WDFTCa computes a similar Hotelling’s T^2-type statistic from successive thresholded batch means of the wavelet-transformed noise vectors using the in-control thresholds; then WDFTCa applies the CUSUM procedure to the resulting T^2-type statistics. Experimentation with several normal and nonnormal test processes revealed that WDFTCa outperformed existing nonadaptive profile-monitoring schemes.

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No description available.

Statistical methods based on nonparametric and distribution-free procedures require the use of order statistics. Order statistics are also used in many parametric estimation and testing problems. With the introduction of modern high speed computers, order statistics have gained more importance in recent years in statistical inference - the main reason being that ranking a large number of observations manually was difficult and time consuming in the past, which is no longer the case at present because of the availability of high speed computers. Also, applications of order statistics require in many cases the use of numerical tables and computer is needed to construct these tables.In this thesis, some basic concepts and results involving order statistics are provided. Typically, application of the Theory of Permanents in the distribution of order statistics are discussed. Further, the correlation coefficient between the smallest observation (Y1) and the largest observation (Y,,) of a random sample of size n from two gamma populations, where (n-1) observations of the sample are from one population and the remaining observation is from the other population, is presented. / Department of Mathematical Sciences

Physical distribution networks are integral parts of modern supply chains. When faced with a question of which node in a network is more important, cost immediately jumps to mind. However, in a world of uncertainty, there are other significant factors which should be considered when trying to answer such a question. The integrity of a network, as well as its robustness are factors that we consider, in making a judgement of importance. We develop algorithms to measure several properties of a class of networks. To accelerate the optimization of multiple related linear programs, we develop a modification of the revised simplex method, which exploits several key aspects to gain efficiency. We combine these algorithms and methods, to give rankings of the relative importance of nodes in networks. In order to better understand the usefulness of our method, we analyse the effect parameter changes have on the relative importance of nodes. We present a large, realistic network, whose nodes we rank in importance. We then vary the network's parameters and observe the impact of each change.

Variable Selection has always been a very important problem in statistics. We often meet situations where a huge data set is given and we want to find out the relationship between the response and the corresponding variables. With a huge number of variables, we often end up with a big model even if we delete those that are insignificant. There are two reasons why we are unsatisfied with a final model with too many variables. The first reason is the prediction accuracy. Though the prediction bias might be small under a big model, the variance is usually very high. The second reason is interpretation. With a large number of variables in the model, it's hard to determine a clear relationship and explain the effects of variables we are interested in. A lot of variable selection methods have been proposed. However, one disadvantage of variable selection is that different sizes of model require different tuning parameters in the analysis, which is hard to choose for non-statisticians. Xin and Zhu advocate variable ranking instead of variable selection. Once variables are ranked properly, we can make the selection by adopting a threshold rule. In this thesis, we try to rank the variables using Least Angle Regression (LARS). Some shrinkage methods like Lasso and LARS can shrink the coefficients to zero. The advantage of this kind of methods is that they can give a solution path which describes the order that variables enter the model. This provides an intuitive way to rank variables based on the path. However, Lasso can sometimes be difficult to apply to variable ranking directly. This is because that in a Lasso solution path, variables might enter the model and then get dropped. This dropping issue makes it hard to rank based on the order of entrance. However, LARS, which is a modified version of Lasso, doesn't have this problem. We'll make use of this property and rank variables using LARS solution path.

Zugl.: Diplomarbeit.

Thesis (Ph. D.)--University of Iowa, 2007. / Supervisor: W. Nick Street. Includes bibliographical references (leaves 83-89).

Ingeniero Comercial, Mención Administración / El presente estudio busca determinar si el ranking relativo escolar in uye signi cativamente en los salarios de las personas. El concepto de ranking relativo se re ere a la ubicaci on alcanzada por un individuo dentro de su generaci on de ense~nanza media, calculada a partir del puntaje NEM1. Postulamos que esta variable captura caracter sticas personales como nivel de esfuerzo, adem as de conocimientos y habilidades cognitivas, valoradas por el mercado laboral. Para este estudio se utiliz o la base de datos de Trabajando.com cruzada con la base de datos del Departamento de Evaluaci on, Medici on y Registro Educacional de Chile (DEMRE) que permite relacionar informaci on laboral y logros acad emicos. A partir de los resultados, se concluye que el ranking relativo escolar in uye signi cativamente s olo para el 10% superior de los egresados de cada promoci on de ense~nanza media, teniendo una in uencia de 7,6% en los salarios. Si se considera el 5% superior el retorno esperado aumenta a un 8,2 %. Ambos resultados controlados entre otras variables por carrera estudiada, puntaje PSU y tipo de colegio. Esto resulta importante, pues muestra una in uencia signi cativa del ranking relativo escolar en el mercado laboral 10 a~nos despu es de terminados los estudios en el colegio2, apuntando a que esta variable captura la presencia de rasgos de nitivos de una persona tal como el nivel de esfuerzo. Este hallazgo, adem as, respalda la idea de complementar el sistema de selecci on universitaria tradicional, incluyendo el ranking relativo escolar como variable de admisi on.