The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis
This new material is concerned with the theory and applications of probability, statistics and analysis of canonical moments. It provides a powerful tool for the determination of optimal experimental designs, for the calculation of the main characteristics of random walks, and for other moment problems appearing in probability and statistics.
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Analysis application approximate argument assertion assume calculation called canonical moments Chapter Chebyshev polynomials coefficients Consequently consider continued fraction converges Corollary corresponding criterion D-optimal defined definition denote density depends determinants discriminating design discussion distribution equal equations equivalent estimate example exists expansion expression finite follows formula function given gives holds identity implies induction integral interest interval kind Lemma linear lower masses matrix maximizes mean Methods monic nonnegative Note numerator Observing obtained optimal design orthogonal polynomials parameter polynomial regression positive prior probability measure problem Proof properties proves provides random walk recursive relation respect result roots satisfy sequence sequence of canonical shown shows simple solution space spectral measure Statistical Stieltjes transform support points symmetric Theorem theory transition probabilities trigonometric uniform unique upper vector weights yields zeros
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