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We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.
A class of limit distributions for quadratic forms of normal stochastic variables
Sevastyanov, B. A · 1961
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On the convergence to normality of quadratic forms in independent variables
Whittle, P · 1964
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Maximum-likelihood estimation for the mixed analysis of variance model
Hartley, H. O · 1967
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A bound on tail probabilities for quadratic forms in independent random variables
Hanson, D. L · 1971
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A trace inequality of John von Neumann
Mirsky, L · 1975
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Maximum likelihood approaches to variance component estimation and to related problems
Harville, D. A · 1977
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Central limit theorem for integrated square error of multivariate nonparametric density estimators
Hall, P · 1984
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An analog of the Cauchy-Schwarz inequality for Hadamard products and unitarily invariant norms
Horn, R. A · 1990
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Variance Components
Searle, S. R · 1992
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Asymptotic properties of restricted maximum likelihood (REML) estimates for hierarchical mixed linear models
Richardson, A. M · 1994
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REML estimation: Asymptotic behavior and related topics
Jiang, J · 1996
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Asymptotic properties of the empirical BLUP and BLUE in mixed linear models
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Lehmann, E. L · 1998
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Van der Vaart, A. W · 2000
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Convergence rates of spectral distributions of large sample covariance matrices
Accurate estimation of heritability in genome wide studies using random effects models
Golan, D · 2011
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A tail inequality for quadratic forms of subgaussian random vectors
Hsu, D · 2012
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Speed, D · 2012
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Zaitlen, N. A · 2012
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Mixed Models: Theory and Applications with R
Demidenko, E · 2013
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Hanson-Wright inequality and sub-gaussian concentration
Rudelson, M · 2013
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