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Methods Of Nonparametric Multivariate Ranking And Selection, Jeremy Entner
Methods Of Nonparametric Multivariate Ranking And Selection, Jeremy Entner
Mathematics - Dissertations
In a Ranking and Selection problem, a collection of k populations is given which follow some (partially) unknown probability distributions. The problem is to select the "best" of the k populations where "best" is well defined in terms of some unknown population parameter. In many univariate parametric and nonparamentric settings, solutions to these ranking and selection problems exist. In the multivariate case, only parametric solutions have been developed. We have developed several methods for solving nonparametric multivariate ranking and selection problems. The problems considered allow an experimenter to select the "best" populations based on nonparametric notions of dispersion, location, and …
Extension Properties Of Pluricomplex Green Functions, Sidika Zeynep Ozal
Extension Properties Of Pluricomplex Green Functions, Sidika Zeynep Ozal
Mathematics - Dissertations
In 1985, Klimek introduced an extremal plurisubharmonic function on bounded domains in Cn that generalizes the Green's function of one variable. This function is called the pluricomplex Green function of Ω with logarithmic pole at a and is denoted by gΩ(.,a). The aim of this thesis was to investigate the extension properties of gΩ(.,a). Let Ω0 be a bounded domain of Cn and E be a compact subset of Ω0 such that Ω : = Ω0 E is connected. In general, gΩ(.,a) cannot be extended as a pluricomplex Green function to any subdomain of …