Quadratic prediction problems in finite populations

Liu, Xu-Qing; Rong, Jian-Ying

doi:10.1016/j.spl.2006.08.015

Cited by 11 publications

(15 citation statements)

References 9 publications

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“…Y HY, provided that Y 1 is the only obtainable vector of variables. Actually, being similar to [6], one can readily conclude that:…”

Section: Oiqu Predictor For Y Hymentioning

confidence: 75%

“…Sections 2 and 3 are clearly generalizations of Liu and Rong [6] in some sense. Consider now a growth curve model, denoted by…”

Section: Discussionmentioning

confidence: 96%

“…Here, we will use the method applied by Liu and Rong [6] to derive two predictors. One is called the OIQU predictor satisfying Invariance, Unbiasedness and Minimality, and the other is called the OIQB predictor satisfying Invariance and Minimality.…”

Section: Optimal Predictors For F(h Y)mentioning

confidence: 99%

“…Recently, Liu and Rong [6] studied a new problem of quadratic prediction for the population quadratic quantities like f (y) = y Hy with H ∈ R n satisfying HX = 0. They proposed two notions of optimal invariant quadratic unbiased (OIQU) predictor and optimal invariant quadratic (potentially) biased (OIQU) predictor.…”

Section: Introductionmentioning

confidence: 99%

“…Secondly, we investigate the problem of predicting some particular functions of Y HY, of form f (H, Y) = τ (Y HY), such as a Y HYb, tr(Y HY), and so on. It is not difficult to see that the no less than three proposed problems are all extensions, in different ways, of Liu and Rong [6]. We will derive the expressions of optimal predictors (in a sense) for them.…”

Section: Introductionmentioning

confidence: 99%

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Quadratic prediction problems in multivariate linear models

Liu

Wang

Rong

2009

Journal of Multivariate Analysis

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a b s t r a c tLinear and quadratic prediction problems in finite populations have become of great interest to many authors recently. In the present paper, we mainly aim to extend the problem of quadratic prediction from a general linear model, of form y = Xβ + e, e ∼ N (0, σ 2 V), to a multivariate linear model, denoted by. . , y q ). Firstly, the optimal invariant quadratic unbiased (OIQU) predictor and the optimal invariant quadratic (potentially) biased (OIQB) predictor of Y HY for any particular symmetric nonnegative definite matrix H satisfying HX = 0 are derived.Secondly, we consider predicting a Y HYb and tr(Y HY). The corresponding restricted OIQU predictor and restricted OIQB predictor for them are given. In addition, we also offer four concluding remarks. One concerns the generalization of predicting a Y HYb and tr(Y HY), and the others are concerned with three possible extensions from multivariate linear models to growth curve models, to restricted multivariate linear models, and to matrix elliptical linear models.

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“…Y HY, provided that Y 1 is the only obtainable vector of variables. Actually, being similar to [6], one can readily conclude that:…”

Section: Oiqu Predictor For Y Hymentioning

confidence: 75%

“…Sections 2 and 3 are clearly generalizations of Liu and Rong [6] in some sense. Consider now a growth curve model, denoted by…”

Section: Discussionmentioning

confidence: 96%

Section: Optimal Predictors For F(h Y)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quadratic prediction problems in multivariate linear models

Liu

Wang

Rong

2009

Journal of Multivariate Analysis

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Quadratic prediction and quadratic sufficiency in finite populations

Liu

Wang

Rong

2009

Journal of Multivariate Analysis

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AMS 2000 subject classifications: 60G25 15A09 62F10 Keywords: Finite population Linear model Nonnegativity OIQBP OIQUP Optimal invariant quadratic (potentially) biased predictor Optimal invariant quadratic unbiased predictor Quadratic prediction Quadratic sufficiency a b s t r a c tThe problem of quadratic prediction for population quadratic quantities in finite populations has been considered in the literature. In this paper, we mainly aim at extending the ordinary quadratic prediction problems to a general case, and derive the representations of the two essentially unique optimal predictors: one is an optimal invariant quadratic unbiased predictor, and the other is an optimal invariant quadratic (potentially) biased predictor. Further, we show that the two predictors are nonnegative and reasonable by considering an extreme situation, and apply resulting conclusions to a special model with a compound symmetric variance matrix. In addition, we propose a notion of quadratic sufficiency with regard to the optimal prediction problems by employing materials derived in the first part, and investigate corresponding characterizations in detail.

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Admissible prediction in superpopulation models with random regression coefficients under matrix loss function

Xu¹,

Yu²

2012

Journal of Multivariate Analysis

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Quadratic prediction problems in finite populations

Cited by 11 publications

References 9 publications

Quadratic prediction problems in multivariate linear models

Quadratic prediction problems in multivariate linear models

Quadratic prediction and quadratic sufficiency in finite populations

Admissible prediction in superpopulation models with random regression coefficients under matrix loss function

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