Variance approximations for estimators of fixed and random effects in mixed linear models
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The article was published on 1979-01-01 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Generalized linear mixed model & Random effects model.read more
Citations
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Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models
TL;DR: In this article, the true values of the variance ratios are replaced by estimated values, and the mean squared errors of the estimators of the fixed and random effects increase in size.
Journal ArticleDOI
A Quasi-Empirical Bayes Method for Small Area Estimation
TL;DR: In this article, an empirical Bayes-type approach for small area estimation based only on the specification of a set of conditionally independent hierarchical mean and variance functions describing the first two moments of the process generating the data is presented.
References
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Book
Theory of probability
Harold Jeffreys,R. Bruce Lindsay +1 more
TL;DR: In this paper, the authors introduce the concept of direct probabilities, approximate methods and simplifications, and significant importance tests for various complications, including one new parameter, and various complications for frequency definitions and direct methods.
Book
Testing statistical hypotheses
TL;DR: The general decision problem, the Probability Background, Uniformly Most Powerful Tests, Unbiasedness, Theory and First Applications, and UNbiasedness: Applications to Normal Distributions, Invariance, Linear Hypotheses as discussed by the authors.
Journal ArticleDOI
The Analysis of Variance
TL;DR: In this paper, the basic theory of analysis of variance by considering several different mathematical models is examined, including fixed-effects models with independent observations of equal variance and other models with different observations of variance.
Journal ArticleDOI
A Rapidly Convergent Descent Method for Minimization
Roger Fletcher,M. J. D. Powell +1 more
TL;DR: A number of theorems are proved to show that it always converges and that it converges rapidly, and this method has been used to solve a system of one hundred non-linear simultaneous equations.
Book
Optimal Statistical Decisions
TL;DR: In this article, the authors present a survey of probability theory in the context of sample spaces and decision problems, including the following: 1.1 Experiments and Sample Spaces, and Probability 2.2.3 Random Variables, Random Vectors and Distributions Functions.