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Arseni Seregin

  1. Uniqueness of the maximum likelihood estimator for k-monotone densities.

    Ср, 01/13/2010 - 16:01 — SomNambul
    Authors: Arseni Seregin
    Subjects: Statistics
    Abstract

    We prove uniqueness of the maximum likelihood estimator for the class of
    k-monotone densities.

  2. Nonparametric estimation of multivariate convex-transformed densities.

    Втр, 11/24/2009 - 16:01 — SomNambul
    Authors: Arseni Seregin, Jon A. Wellner
    Subjects: Statistics
    Abstract

    We study estimation of multivariate densities $p$ of the form $p(x) =
    h(g(x))$ for $x \in R^d$ and for a fixed function $h$ and an unknown convex
    function $g$. The canonical example is $h(y) = e^{-y}$ for $y \in R$; in this
    case the resulting class of densities $$\mathcal{P}(e^{-y}) = \{p = \exp(-g) :
    g is convex \}$$ is well-known as the class of log-concave densities. Other
    functions $h$ allow for classes of classes of densities with heavier tails than
    the log-concave class.

  3. Empirically corrected estimation of complete-data population summaries under model misspecification.

    Пт, 11/06/2009 - 16:01 — SomNambul
    Authors: Arseni Seregin, Vladimir N. Minin, John D. O'Brien
    Subjects: Methodology
    Abstract

    Inference problems with incomplete observations often aim at estimating
    population-level properties of complete data. We introduce a simple empirical
    correction that provides partial protection against model misspecification
    during such estimation. Unlike nonparametric or semiparametric techniques, our
    empirical correction does not produce consistent estimates. Instead, our method
    first fits a misspecified parametric model, whose plug-in estimate of the
    quantity of interest is naturally inconsistent.

  4. On the Grenander estimator at zero.

    Пт, 09/11/2009 - 19:12 — SomNambul
    Authors: Fadoua Balabdaoui, Hanna K. Jankowski, Marios Pavlides, Arseni Seregin, Jon A. Wellner
    Subjects: Statistics
    Abstract

    We establish limit theory for the Grenander estimator of a monotone density
    near zero. In particular we consider the situation when the true density $f_0$
    is unbounded at zero, with different rates of growth to infinity. In the course
    of our study we develop new switching relations by use of tools from convex
    analysis. The theory is applied to a problem involving mixtures.

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