Week of April 13 - April 17

Monday, April 13

11:30 MATHEMATICS EDUCATION SEMINAR  - Room 447 MSC
      Oxana Grinevitch, Mathematics and Statistics, BGSU   
      "Skinner, behaviorism and mathematics learning"

 2:30 ALGEBRA SEMINAR  - Room 447 MSC
      Sergey Shpectorov, Mathematics and Statistics, BGSU 
      "Landazuri-Seitz-Zalesskii bound"

 2:30 ANALYSIS SEMINAR  - Room 459 MSC
      Neal Carothers, Mathematics and Statistics, BGSU 
      "Riesz bases II"
      Abstract: We will discuss Bari's Theorem and the Kothe-Toeplitz
        Theorem on unconditional bases in Hilbert space.  This is a
        continuation of last week's talk, but is based largely on
        elementary principles.  The talk should be accessible to any
        student in MATH 766.
                
 3:30 LUKACS LECTURE  - Room 459 MSC
      C. R. Rao, Distinguished Lukacs Professor, BGSU
      "Statistical solutions to matrix problems"
      Abstract: Most of the propositions in the theory of Linear
        Estimation and Multivariate Analysis are proved using results
        of Matrix Algebra.  It is shown that some of the key results
        in Matrix Algebra can be derived from certain propositions in
        mathematical statistics, whose derivation does not depend on
        matrix theory.

        We exploit two results in mathematical statistics for this
        purpose.  One is that Fisher information in the whole sample
        is not less than the information in a statistic.  Another is
        that the variance-covariance matrix of a vector random
        variable is non-negative definite.

        The following results will be discussed: Convexity of A
        inverse and A squared in the space of positive-definite
        matrices; Milne's inequality; Non-negative definiteness of
        Schur complement, Hadamard and Kronecker products of matrices;
        Kantorovich inequality using linear programming and so on.

Tuesday, April 14

11:30 GRADUATE STUDENT SEMINAR  - Room 459 MSC
      *** Note change of time ***
      John Steele, Mathematics and Statistics, BGSU 
      "Limiting distributions for hierarchical structures"
      All are welcome to attend.
      Abstract: Limiting distributions have been a focus of study in
        probability for some time.  The Central Limit Theorem for sums
        of random variables and the asymptotic normality of many other
        statistics are often used to provide useful approximations of
        probabilities.  In the field of Reliability the well known
        limiting distributions for minimum and maximum of observations
        are often used.  These are usually discussed in terms of
        limiting distributions arising from "series" structures in the
        case of minimum observations and "parallel" structures in
        terms of maximum observations.  The type of structure relates
        to the actual design of a system or network.  In this talk I
        shall generalize some of the notions used in determining these
        limiting distributions to other structures beyond the series
        and parallel cases.  The idea of a limiting distribution will
        come from the repeated composition of the structure upon
        itself.  For the series and parallel cases this yields results
        consistent with those already well known.  I'll be able to
        show that for most structures there is an analytic limiting
        distribution.  While necessary and sufficient conditions for
        distributions to be within the domain of attraction of a
        particular limiting distribution do still remain elusive I
        will show some conditions of sufficiency.  Along the way to
        these results interesting observations concerning coherent
        structures and their related reliability polynomials are
        highlighted.

 2:30 SCIENTIFIC COMPUTATION SEMINAR  - Room 459 MSC

 2:30 MAPLE WORKSHOP  - Scientific Computing Lab, MSC
      John Gresser, Mathematics and Statistics, BGSU. 

 3:30 FACULTY MEETING  - Room 459 MSC
      Followup on the department retreat last Saturday.

Wednesday, April 15

11:30 MATHEMATICS EDUCATION SEMINAR  - Room 447 MSC
      Oxana Grinevitch, Mathematics and Statistics, BGSU 
      "Skinner, behaviorism and mathematics learning"
      
Thursday, April 16

 1:00 STATISTICAL COMPUTING SEMINAR  - Room 459 MSC
      Jane Harvill, Applied Statistics and Operations Research, BGSU
      "Density estimation"

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Monday, April 20

 3:30 LUKACS LECTURE  - Room 459 MSC
      C. R. Rao, Distinguished Lukacs Professor, BGSU
      "Pre- and Post-Least-Squares: The Emergence of Robust Estimation" 
      Abstract: From the time of Ptolemy, astronomers were faced with
        the problem of obtaining best estimates of unknown parameters
        from measurements subject to error.  Various attempts, partly
        objective and partly subjective were made during the last five
        centuries, which finally led to the discovery of the method of
        least squares (LSE) in the beginning of the last century in
        which Gauss (1777-1855) and Laplace (1749-1827) played major
        roles.  Subsequent contributions by Markoff, Aitken, Bose, and
        Rao provided generalizations of LSE to cover a number of
        practical situations.  A historical account of the development
        of LSE will be presented.

        LSE has nice properties when errors are normally distributed.
        However, they are sensitive to departures from normality and
        the presence of outliers.  Some of the latest methods in what
        is called M-estimation, which are robust to model deviations
        and outliers will be discussed.

Friday, April 24
 
 9:00 Lukacs Symposium begins  - Room 115 Olscamp Hall

Saturday, April 25

 8:00 Lukacs Symposium continues

Sunday, April 26

 8:00 Lukacs Symposium continues

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