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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...
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...
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 ...
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 ...
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 ...
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...

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