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Consider a polynomial regression situation on an interval and also a robustness-type formulation of Stigler's. A technique involving canonical moments is discussed and some explicit solutions are given. [ABSTRACT FROM AUTHOR]

The problem of estimating the slope of a polynomial regression at a fixed point of the experimental region such that (a) the variance of the least-square estimate of the slope at the fixed point is a minimum and {b) the average variance of the least-square estimate of the slope is a minimum is discussed in this paper. In general these designs can be obtained using Kiefer-Wolfowitz [5] characterization of c-optimal designs, Federov [2] characterization of L-optimal designs, and Studden's [10] generalization of the Elfving Theorem [1]. After presenting a brief review of these characterization theorems, specific illustrations for the quadratic and cubic regressions are presented in detail. [ABSTRACT FROM AUTHOR]

In this paper we study the connection between matrix measures and random walks with a block tridiagonal transition matrix. We derive sufficient conditions such that the blocks of the n-step block tridiagonal transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure. Several stochastic properties of the processes are characterized by means of this matrix measure. In many cases this measure is supported in the interval [-1, 1]. The results are illustrated by several examples including random walks on a grid and the embedded chain of a queuing system. [ABSTRACT FROM AUTHOR]

The article discusses a study in which the authors built, via computer models, designs with good prediction accuracy. The authors studied an asymptotic form of the Gussian correlation function for the stochastic process where the correlation tends to unity. After illustrating that the limiting best linear unbiased predictor involves Lagrange interpolating polynomials, they developed optimal designs based on reducing the limiting, integrated mean squared error of prediction. They then illustrated through examples how these designs make good predictors.