Concentration of empirical distribution functions for dependent data under analytic hypotheses

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Concentration of empirical distribution functions for dependent data under analytic hypotheses

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2013-05

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The concentration property of empirical distribution functions is studied under the Levy distance for dependent data whose joint distribution satisfies analytic conditions expressed via Poincare-type and logarithmic Sobolev inequalities. The concentration results are then applied to the following two general schemes. In the first scheme, the data are obtained as coordinates of a point randomly selected within given convex bodies (and more generally -- when the sample obeys a log-concave distribution). In the second scheme, the data represent eigenvalues of symmetric random matrices whose entries satisfy the indicated analytic conditions.

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University of Minnesota Ph.D. dissertation. May 2013. Major: Mathematics. Advisor: Sergey G. Bobkov. 1 computer file (PDF); ii, 65 pages, appendix A-B.

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Kim, Ji Hee. (2013). Concentration of empirical distribution functions for dependent data under analytic hypotheses. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/153632.

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