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Best quadratic predictions in finite populations

机译:有限总体中的最佳二次预测

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摘要

For a finite population and the resulting linear model Y=Xβ+e, the problem of the optimal invariant quadratic predictors including optimal invariant quadratic unbiased predictor and optimal invariant quadratic (potentially) biased predictor for the population quadratic quantities, f(H)=Y′HY , is of interest and has been previously considered in the literature for the case of HX=0. However, the special case does not contain all of situations at all. So, predicting f(H) in general situations may be of particular interest. In this paper, we make an effort to investigate how to offer a good predictor for f(H), not restricted yet to the mentioned case. Permutation matrix techniques play an important role in handling the process. The expected predictors are finally derived. In addition, we mention that the resulting predictors can be viewed as acceptable in all situations.
机译:对于一个有限的人口和由此产生的线性模型Y =Xβ+ e,最优不变二次预测变量的问题包括最优不变二次无偏预测变量和最优不变二次(潜在)有向变量的人口二次变量f(H)=Yâ €²HY是有意义的,以前在文献中已将HX = 0的情况考虑在内。但是,特殊情况根本不包含所有情况。因此,在一般情况下预测f(H)可能特别有意义。在本文中,我们努力研究如何为f(H)提供良好的预测指标,但不仅限于上述情况。置换矩阵技术在处理过程中起着重要作用。最终得出预期的预测变量。此外,我们提到,在所有情况下,可以将所得的预测变量视为可接受的。

著录项

  • 来源
  • 作者

    Xu-Qing Liu;

  • 作者单位

    Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai'an, 223003, People's Republic of China;

  • 收录信息 美国《科学引文索引》(SCI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

  • 入库时间 2022-08-18 00:58:20

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