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An Approximate Approach to E-optimal Designs for Weighted Polynomial Regression by Using Tchebycheff Systems and Orthogonal Polynomials
An Approximate Approach E-optimal Designs Weighted Polynomial Regression Using Tchebycheff Systems Orthogonal Polynomials
2013/4/28
In statistics, experimental designs are methods for making efficient experiments. E-optimal designs are the multisets of experimental conditions which minimize the maximum axis of the confidence ellip...
The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory
The infinite divisibility orthogonal polynomials a constant recursion formula
2009/9/21
We calculate Voicdescu's R-transform of the compactly
supported probability measure on R induced from the orthogonal
polynomials with a constant recursion formula, and investigate its
infinite divi...
Generating functions of orthogonal polynomials and Szego-Jacobi parameters
Interacting Fock space probability measure orthogonal polynomial Szegii-Jacobi parameters
2009/9/21
In this paper, we present a more direct way to compute
the SzeggJacobi parameters from a generating function than that in
[S] and [6]. Our study is motivated by the notions of one-mode interacting
...
Gibbs Sampling，Exponential Families and Orthogonal Polynomials
Gibbs sampler running time analyses exponential families conjugate priors location families orthogonal polynomials
2010/4/30
We give families of examples where sharp rates of convergence
to stationarity of the widely used Gibbs sampler are available.
The examples involve standard exponential families and their conjugate
...
Comment：Gibbs Sampling，Exponential Families and Orthogonal Polynomials
Comment Gibbs Sampling Exponential Families Orthogonal Polynomials
2010/4/30
Let K be a reversible Markov kernel on a measurable
space (S,B) with stationary distribution P.
Regard K as a linear operator, K:L2(P)→L2(P),
and suppose that L2(P) admits an orthonormal basis
of ...
Rejoinder：Gibbs Sampling，Exponential Families and Orthogonal Polynomials
Rejoinder Gibbs Sampling Exponential Families Orthogonal Polynomials
2010/4/30
We are thankful to the discussants for their hard, interesting
work. The main purpose of our paper was to give reasonably sharp rates
of convergence for some simple examples of the Gibbs sampler. We...