# Quotient of information matrices in comparison of linear experiments for quadratic estimation

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1599-1605
- ISSN: 2391-5455

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topCzesław Stępniak. "Quotient of information matrices in comparison of linear experiments for quadratic estimation." Open Mathematics 15.1 (2017): 1599-1605. <http://eudml.org/doc/288322>.

@article{CzesławStępniak2017,

abstract = {The ordering of normal linear experiments with respect to quadratic estimation, introduced by Stępniak in [Ann. Inst. Statist. Math. A 49 (1997), 569-584], is extended here to the experiments involving the nuisance parameters. Typical experiments of this kind are induced by allocations of treatments in the blocks. Our main tool, called quotient of information matrices, may be interesting itself. It is known that any orthogonal allocation of treatments in blocks is optimal with respect to linear estimation of all treatment contrasts. We show that such allocation is, however, not optimal for quadratic estimation.},

author = {Czesław Stępniak},

journal = {Open Mathematics},

keywords = {Normal linear experiment; Comparison of experiments for quadratic estimation; Nuisance parameter; Quotient of information matrices; Orthogonal block design; Nonoptimality for quadratic estimation},

language = {eng},

number = {1},

pages = {1599-1605},

title = {Quotient of information matrices in comparison of linear experiments for quadratic estimation},

url = {http://eudml.org/doc/288322},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Czesław Stępniak

TI - Quotient of information matrices in comparison of linear experiments for quadratic estimation

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1599

EP - 1605

AB - The ordering of normal linear experiments with respect to quadratic estimation, introduced by Stępniak in [Ann. Inst. Statist. Math. A 49 (1997), 569-584], is extended here to the experiments involving the nuisance parameters. Typical experiments of this kind are induced by allocations of treatments in the blocks. Our main tool, called quotient of information matrices, may be interesting itself. It is known that any orthogonal allocation of treatments in blocks is optimal with respect to linear estimation of all treatment contrasts. We show that such allocation is, however, not optimal for quadratic estimation.

LA - eng

KW - Normal linear experiment; Comparison of experiments for quadratic estimation; Nuisance parameter; Quotient of information matrices; Orthogonal block design; Nonoptimality for quadratic estimation

UR - http://eudml.org/doc/288322

ER -