Thesis (M.S.)--University of Missouri--Rolla, 2007. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed December 11, 2007) Includes bibliographical references (p. 50-51).

No description available.

Thesis (Ph. D., Biological and Agricultural Engineering)--University of Idaho, June 2007. / Major professor: Jan Boll. Includes bibliographical references. Also available online (PDF file) by subscription or by purchasing the individual file.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1951. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 96-98).

Thesis (M.S.)--University of Wisconsin--Madison, 1981. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 48-49).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 293-310).

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Subsampling is an important method in the analysis of Big Data. Subsample size determination (SSSD) plays a crucial part in extracting information from data and in breaking<br>the challenges resulted from huge data sizes. In this thesis, (1) Sample size determination<br>(SSD) is investigated in multivariate parameters, and sample size formulas are obtained for<br>multivariate normal distribution. (2) Sample size formulas are obtained based on concentration inequalities. (3) Improved bounds for McDiarmid’s inequalities are obtained. (4) The<br>obtained results are applied to nonuniform subsampling in Big Data high dimensional linear<br>regression. (5) Numerical studies are conducted.<br>The sample size formula in univariate normal distribution is a melody in elementary<br>statistics. It appears that its generalization to multivariate normal (or more generally multivariate parameters) hasn’t been caught much attention to the best of our knowledge. In<br>this thesis, we introduce a definition for SSD, and obtain explicit formulas for multivariate<br>normal distribution, in gratifying analogy of the sample size formula in univariate normal.<br>Commonly used concentration inequalities provide exponential rates, and sample sizes<br>based on these inequalities are often loose. Talagrand (1995) provided the missing factor to<br>sharpen these inequalities. We obtained the numeric values of the constants in the missing<br>factor and slightly improved his results. Furthermore, we provided the missing factor in<br>McDiarmid’s inequality. These improved bounds are used to give shrunken sample sizes <br>

No description available.

No description available.