Browsing by Subject "Concentration of measure"

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    Concentration of empirical distribution functions for dependent data under analytic hypotheses
    (2013-05) Kim, Ji Hee
    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.