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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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Linear Mixed Models: Part I
The best way to understand a linear mixed modelLinear mixed model , or mixed linear model in some earlier literature, is to first recall a linear...
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Linear Mixed Models: Part II
The previous chapter dealt with point estimation and related problems in linear mixed models. In this section, we consider a different type of...
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Generalized Linear Mixed Models: Part I
For the most part, linear mixed models have been used in situations where the observations are continuous. However, oftentimes in practice the...
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Fisher Scoring for crossed factor linear mixed models
The analysis of longitudinal, heterogeneous or unbalanced clustered data is of primary importance to a wide range of applications. The linear mixed...
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Exact distributions of statistics for making inferences on mixed models under the default covariance structure
At this juncture when mixed models are heavily employed in applications ranging from clinical research to business analytics, the purpose of this...
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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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On drawbacks of least squares Lehmann–Scheffé estimation of variance components
Estimation of variance components is one of the basic problems in linear models with mixed effects, and a vast literature exists on the subject....
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Inference for Variance–Covariance Parameters
In Chaps. 11 and 13 , we obtained BLUEs for estimable linear functions under the Aitken model and BLUPs for predictable linear functions under...
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Various Frailty Models
The shared frailty model is relevant to event time of the related individuals, similar organs and repeated measurements. In this model individuals...
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Some Properties of Linear Prediction Sufficiency in the Linear Model
A linear statistic \(\mathbf {F}\mathbf {y}\)...
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Mixed-Effects Survival Models
The frailty model accounts for dependence between survival times, by including a random effect acting multiplicatively on the individual hazard rate.
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Fast and robust estimators of variance components in the nested error model
Usual fitting methods for the nested error linear regression model are known to be very sensitive to the effect of even a single outlier. Robust...
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H-Likelihood Approach to Random-Effect Models
In this chapter, we introduce an h-likelihood approach to the general class of statistical models with random effects. Consider a linear mixedLinear...
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Efficient estimation of variance components in nonparametric mixed-effects models with large samples
Linear mixed-effects (LME) regression models are a popular approach for analyzing correlated data. Nonparametric extensions of the LME regression...
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Array Normal Model and Incomplete Array Variate Observations
Missing data present an important challenge when dealing with high-dimensional data arranged in the form of an array. The main purpose of this...
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Further Developments on the Henderson Trend-Cycle Filter
The linear filter developed by Henderson is the most widely applied to estimate the trend-cycle component in seasonal adjustment software such as the...
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Linear Filters Seasonal Adjustment Methods: Census Method II and Its Variants
The best known and most often applied seasonal adjustment methods are based on smoothing linear filters or moving averages applied sequentially by...
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The link between the mixed and fixed linear models revisited
Haslett and Puntanen (Stat Pap 51:465–475,
2010 ) studied the links between the linear mixed model and a particular extended linear model including...