By Ams Special Session on Algebraic Methods in Statistics, Marlos A. G. Viana, Donald St. P. Richards (ed.)
Algebraic equipment and arguments in facts and likelihood are renowned, from Gauss' least squares precept via Fisher's approach to variance decomposition. The relevance of group-theoretic arguments, for instance, turned obvious within the Eighties. Such thoughts remain of curiosity this day, in addition to different advancements, akin to using graph thought in modelling advanced stochastic systems.This quantity relies on lectures provided on the AMS unique consultation on Algebraic tools and facts held on the college of Notre Dame (Indiana) and on contributed articles solicited for this quantity. The articles are meant to foster verbal exchange among representatives of the various clinical parts within which those features are applied and to additional the craze of using algebraic equipment within the parts of facts and chance. this can be one among few volumes dedicated to the topic of algebraic equipment in information and chance. the big variety of subject matters coated during this quantity demonstrates the lively point of study and possibilities ongoing in those components
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Additional info for Algebraic Methods in Statistics and Probability
By the term "distribution system" we understand a class of distributions constructed by means of a - -) For the sake of clarity, and to simplify practical manipulation, preference is given to systems which as far as possible contain not more than one distribution for each pair, YI> Y2 . The "suprasystem" proposed by Savageau (1982), in which a large variety of different distribution systems are produced by a common construction rule, is unsuitable for use in simulation studies. We shall, moreover, ignore distribution systems which describe only one line in the (Yh Y2)-plane.
7 (1976) 51-68. LI, K. , NOTZ, W. Robust designs for nearly linear regr('ssion. T. Statist. Plann. 1n[('r. 6 (19fl2) 1:1~-151. MARCUS, M. , SACKS, J. Robust designs for regression problems. Statistical Decision Theory and Related Topics II. Academic, New York, 1977, 245-268. PESOTCHINSKY, L. Optimal robust designs: Linear regression in R K , Ann. Statist. 10 (1982) 511-525. , YLVISAKER, D. Linear estimation for approximately linear models. Ann. Statist. 6 (1978) 1122-1137. STIGLER, S. M. Optimal ('xp('rimental design for polynomial regression.
The fJ w -mlmmax design s* = ~* «()'2/ (ne 2», w being the uniform measure on [-1/2, 112], is absolutely continuous with respect to Lebesgue measure. d*) sup 1f'(R(d,L,a-'y)) YEr = 00, so that s* does not admit a reasonable interpretation, which was observed by Li and Notz (1982), p. 136. The same objection pertains to the minimax design for estimating the slope of the regression line given by Huber (1975), pp. 295-296. So for nonparametric contaminations one should generally restrict to approximate designs with finite support.
Algebraic Methods in Statistics and Probability by Ams Special Session on Algebraic Methods in Statistics, Marlos A. G. Viana, Donald St. P. Richards (ed.)