Totally positive regression: E-optimal designs

被引：0
作者：
Heiligers B. [1 ]
机构：
[1] Fakultät für Mathematik, Inst. für Math. Stochastik, Universität Magdeburg
来源：
Metrika | 2002年 / 54卷 / 3期
关键词：
Approximate design; Chebyshev approximation; Chebyshev system; E-optimality; Equi-oscillation; Polynomial splines; Scalar optimality; Total positivity; Weighted polynomial regression;
D O I：
10.1007/s184-002-8364-7
中图分类号：
学科分类号：
摘要：
E-optimality of approximate designs in linear regression models is paired with a dual problem of nonlinear Chebyshev approximation. When the regression functions form a totally positive system, then the information matrices of designs for subparameters turn out to be "almost" totally positive, a property which allows to solve the nonlinear Chebyshev problem. Thereby we obtain explicit formulae for E-optimal designs in terms of equi-oscillating generalized polynomials. The considerations unify and generalize known results on E-optimality for particular regression setups.
引用
收藏
页码：191 / 213
页数：22
相关论文
共 42 条
  • [31] Krafft O., A matrix optimization problem, Lin Algebra Appl, 51, pp. 137-142, (1983)
  • [32] Krafft O., On universally optimal designs for regression setups, J Statist Plann Inference, 12, pp. 347-352, (1985)
  • [33] Marshall A.W., Olkin I., Inequalities: Theory of Majorization and Its Applications, (1979)
  • [34] Mitra S.K., Puri M.L., Shorted operators and generalized inverses of matrices, Lin Algebra Appl, 25, pp. 45-56, (1979)
  • [35] Morken K., Total positivity and splines, Total Positivity and Its Applications, pp. 47-84, (1996)
  • [36] Murty V.N., Optimal designs with a tchebycheffian spline regression function, Ann Math Statist, 42, pp. 643-649, (1971)
  • [37] Pukelsheim F., Optimal Design of Experiments, (1993)
  • [38] Pukelsheim F., Torsney B., Optimal weights for experimental design on linearly independent support points, Ann Statist, 19, pp. 1614-1625, (1991)
  • [39] Pukelsheim F., Studden W.J., E-optimal designs for polynomial regression, Ann Statist, 21, pp. 402-415, (1993)
  • [40] Seneta E., Non-negative Matrices and Markov Chains (2nd Edition), (1981)
12345