Includes bibliographical references (p. 38-40).

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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

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

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In this thesis, we investigate how well we can reconstruct the best rank-? approximation of a large matrix from a small number of its entries. We show that even if a data matrix is of full rank and cannot be approximated well by a low-rank matrix, its best low-rank approximations may still be reliably computed or estimated from a small number of its entries. This is especially relevant from a statistical viewpoint: the best low-rank approximations to a data matrix are often of more interest than itself because they capture the more stable and oftentimes more reproducible properties of an otherwise complicated data-generating model. In particular, we investigate two agnostic approaches: the first is based on spectral truncation; and the second is a projected gradient descent based optimization procedure. We argue that, while the first approach is intuitive and reasonably effective, the latter has far superior performance in general. We show that the error depends on how close the matrix is to being of low rank. Our results can be generalized to the spectral and entrywise error and provide flexible tools for the error analysis of the follow-up computation. Moreover, we derive a high-order decomposition of the error. With an explicit expression of the main error source, we obtain an improved estimate of the linear form. Both theoretical and numerical evidence is presented to demonstrate the effectiveness of the proposed approaches.

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2004. / Includes bibliographical references (p. 65).

Thesis (M.Sc.)--Memorial University of Newfoundland, 2001. / Restricted until October 2004. Bibliography: leaves 99-101.

published_or_final_version / Statistics / Master / Master of Philosophy