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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

High-dimensional statistics : model specification and elementary estimators

Yang, Eunho 16 January 2015 (has links)
Modern statistics typically deals with complex data, in particular where the ambient dimension of the problem p may be of the same order as, or even substantially larger than, the sample size n. It has now become well understood that even in this type of high-dimensional scaling, statistically consistent estimators can be achieved provided one imposes structural constraints on the statistical models. In spite of great success over the last few decades, we are still experiencing bottlenecks of two distinct kinds: (I) in multivariate modeling, data modeling assumption is typically limited to instances such as Gaussian or Ising models, and hence handling varied types of random variables is still restricted, and (II) in terms of computation, learning or estimation process is not efficient especially when p is extremely large, since in the current paradigm for high-dimensional statistics, regularization terms induce non-differentiable optimization problems, which do not have closed-form solutions in general. The thesis addresses these two distinct but highly complementary problems: (I) statistical model specification beyond the standard Gaussian or Ising models for data of varied types, and (II) computationally efficient elementary estimators for high-dimensional statistical models. / text

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