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General Mixed-Effects Models and BLUP
Linear mixed models are widely used in a variety of scientific areas such as small area estimation (Rao and Molina 2015), longitudinal data analysis...
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Empirical BLUE and BLUP
Recall from Sect. 13.5 that E-BLUP, the conventional procedure for predicting a predictable linear function τ = c Tβ + u under the...
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Empirical BLUE and BLUP
This chapter presents exercises on empirical best linear unbiased estimation and empirical best linear unbiased prediction and provides solutions to...
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Predictions Under a System of Linear Regression Models with Correlated Errors
A system of linear regression models that consists of several regression equations is an extension of the linear regression models which allow...
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A Review of the Linear Sufficiency and Linear Prediction Sufficiency in the Linear Model with New Observations
We consider the general linear model $$\mathbf{y} = \mathbf{X} {\pmb {\beta }}+ {\pmb...
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Measuring Uncertainty of Predictors
An important aspect of small area estimation is the assessment of accuracy of the predictors. Under the frequentist approach, this will be...
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Introduction
The term ‘small area’ or ‘small domain’ refers to a small geographical region such as a county, municipality or state, or a small demographic group...
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Bayesian Optimization Approaches for Identifying the Best Genotype from a Candidate Population
Bayesian optimization is incorporated into genomic prediction to identify the best genotype from a candidate population. Several expected improvement...
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Further remarks on constrained over-parameterized linear models
This paper considers comparison problems for dispersion matrices of predictors under two competing linear models with having the same restrictions on...
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Estimating the prevalence of anemia rates among children under five in Peruvian districts with a small sample size
In this paper we attempt to answer the following question: “Is it possible to obtain reliable estimates for the prevalence of anemia rates in...
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Basic Mixed-Effects Models for Small Area Estimation
Statistical inference in the general linear mixed models is explained in the previous chapters. As basic models used in small area estimation, in...
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How the sampling variances affect the linear predictor of the Fay-Herriot model
The Fay-Herriot model can be seen as a linear mixed-effects model, with known within-subject variance parameters. These values are given by the...
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Advanced Theory of Basic Small Area Models
In Chap. 4, we introduced two famous small area models, Fay–Herriot and nested error regression models, and provided basic theory of parameter...
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Optimal designs for prediction in random coefficient regression with one observation per individual
The subject of this work is random coefficient regression models with only one observation per observational unit (individual). An analytical...
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Estimation of poverty and inequality in small areas: review and discussion
Never better said, a correct diagnosis is crucial for patient recovery. In the eradication of poverty, which is the first of the sustainable...
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D-optimal joint best linear unbiased prediction of order statistics
In life-testing experiments, it is often of interest to predict unobserved future failure times based on observed early failure times. A point best...
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Extensions of Basic Small Area Models
The flexibility of the two basic small area models described in Chap. 4 can be limited for practical...
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An Application of Spatio-Temporal Modeling to Finite Population Abundance Prediction
Spatio-temporal models can be used to analyze data collected at various spatial locations throughout multiple time points. However, even with a...
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Computer Experiments
Computer experiments are integrated in modern product and service development activities. Technology is providing advanced digital platforms for...