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  • Thesis

  • Statistical Inference for Single-Index Models

    • Authors: Lin, Wei (2006)

  • With the rapid increase in computing power, nonparametric methods in regression analysis have gained more and more popularity. One major difficulty in a general nonparametric regression model comes from the so-called "curse-of-dimensionality"; the difficulty and inefficiency of smoothing in high-dimensional settings. Hence, scientists seek techniques to reduce the model dimension in order to keep a reasonable level of accuracy for all practical purposes. The single-index model, where the regression function takes the form m(x) = g(O'x), is a natural generalization of the classical linear regression models and a restrictive version of a completely nonparametric model. Most of the statistical analysis in the literature for the single-index models focuses on estimating the index vector...
  • Thesis

  • The Brauer Group of Del Pezzo Surfaces

    • Authors: Carter, Andrea C. (2006)

  • Let S1 be a Del Pezzo surface of degree one over a number field k, and let S1 denote the base-change of S1 over the algebraic closure k of k. We establish a criterion for the existence of a non-trivial element of order five in the Brauer group of S1 in terms of certain Galois stable configurations of exceptional divisors on this surface.
  • Thesis

  • Unramified representations of p-adic groups on spherical varieties

    • Authors: Sakellaridis, Loannis (2006)

  • The description of irreducible representations of a group G can be seen as a question in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G x G by left and right multiplication. For a split p-adic reductive group G over a local non-archimedean field, unramified irreducible smooth representations are in bijection with semisimple conjugacy classes in the "Langlands dual" group. In the first part of this work, we generalize this description to an arbitrary spherical variety X of G as follows: Irreducible quotients of the "unramified" Bernstein component of C°°(X) (or, more generally, CC°(X, LT), where L,y is a G-linear line bundle over X) are in natural almost bijection with (a number of copies of) the quotient of a complex...
  • Thesis

  • Zd Symbolic Dynamics: Coding with an Entropy Inequality

    • Authors: Desai, Angela (2006)

  • In this paper we discuss subsystem and coding results in Zd symbolic dynamics for d > 1. We prove that any Zd shift of finite type with positive topological entropy has a family of subsystems of finite type whose entropies are dense in the interval from zero to the entropy of the original shift. We show a similar result for Zd sofic shifts, and also show every Zd sofic shift can be covered by a Zd shift of finite type arbitrarily close in entropy. We also show that if a Z2 shift of finite type with entropy greater than log N satisfies a certain mixing condition, then it must factor onto the full N-shift.