Some remarks on comparison of predictors in seemingly unrelated linear mixed models

Nesrin Güler; Melek Eriş Büyükkaya

Displaying similar documents to “Some remarks on comparison of predictors in seemingly unrelated linear mixed models”

Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values

Wiktor Oktaba (1998)

Applications of Mathematics

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The aim of this paper is to characterize the Multivariate Gauss-Markoff model $(M G M)$ as in () with singular covariance matrix and missing values. $M G M D P 2$ model and completed $M G M D P 2 Q$ model are obtained by three transformations $D$ , $P$ and $Q$ (cf. ()) of $M G M$ . The unified theory of estimation (Rao, 1973) which is of interest with respect to $M G M$ has been used. The characterization is reached by estimation of parameters: scalar $σ^{2}$ and linear combination $λ^{'} \bar{B}$ ( $\bar{B} = v e c B)$ as in (), (), () as well as by the model of the form ()...

Some $R^{N}$ capacities and applications - the lemma on mixed derivatives revisited

J. Korevaar (1986)

Matematički Vesnik

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ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces

Denny H. Leung, Wee-Kee Tang (2006)

Studia Mathematica

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We investigate the existence of higher order ℓ¹-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space $X = T [{(θ ₙ, ₙ)}_{n = 1}^{\infty}]$ : (1) Every block subspace of X contains an $ℓ ¹ -_{ω}$ -spreading model, (2) The Bourgain ℓ¹-index $I_{b} (Y) = I (Y) > ω^{ω}$ for any block subspace Y of X, (3) $l i m ₘ l i m s u p ₙ θ_{m + n} / θ ₙ > 0$ and every block subspace Y of X contains a block sequence equivalent to a subsequence of the unit vector basis of X. Moreover, if one (and hence all) of these...

The splitting number can be smaller than the matrix chaos number

Heike Mildenberger, Saharon Shelah (2002)

Fundamenta Mathematicae

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Let χ be the minimum cardinality of a subset of $^{ω} 2$ that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of a creature forcing we show that < χ is consistent. We thus answer a question by Vojtáš. We give two kinds of models for the strict inequality. The first is the combination of an ℵ₂-iteration of some proper forcing with adding ℵ₁ random reals. The second kind of models is obtained by adding δ random reals to a model of $M A_{< κ}$ for some δ ∈...

On the existence of exactly one solution of integral equations in the space $L^{P}$ with a mixed norm

Bogdan Rzepecki (1975)

Annales Polonici Mathematici

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Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

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By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant $| σ^{2} \sum |$ in the MGM model $(U, X B, σ^{2} \sum \otimes V)$ , $\sum > 0$ , scalar $σ^{2} > 0$ , with a matrix $V \geq 0$ . A known $n \times p$ random matrix $U$ has the expected value $E (U) = X B$ , where the $n \times d$ matrix $X$ is a known matrix of an experimental design, $B$ is an unknown $d \times p$ matrix of parameters and $σ^{2} \sum \otimes V$ is the covariance matrix of $U, \otimes$ being the symbol...

An example of the equation $u_{t} = u_{x x} + f (x, t, u)$ with distinct maximum and minimum solutions of a mixed problem

W. Mlak (1963)

Annales Polonici Mathematici

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Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures

Philippe Eyssidieux, Carlos Simpson (2011)

Journal of the European Mathematical Society

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Let $X$ be a compact Kähler manifold, $x \in X$ be a base point and $ρ : π_{1} (X, x) \to G L_{N} (C)$ be the monodromy representation of a $𝒞$ -VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at $ρ$ and a variation of mixed Hodge structures whose monodromy is the universal deformation of $ρ$ .

The diagonal mapping in mixed norm spaces

Guangbin Ren, Jihuai Shi (2004)

Studia Mathematica

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For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space $H^{p, q, α} (U ⁿ)$ of the polydisc onto the mixed norm space $H^{p, q, | α | + (p / q + 1) (n - 1)} (U)$ of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.

Monotone Hurwitz Numbers and the HCIZ Integral

I. P. Goulden, Mathieu Guay-Paquet, Jonathan Novak (2014)

Annales mathématiques Blaise Pascal

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In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of $z = 0$ . Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.

A geometric point of view on mean-variance models

Piotr Jaworski (2003)

Applicationes Mathematicae

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This paper deals with the mathematics of the Markowitz theory of portfolio management. Let E and V be two homogeneous functions defined on ℝⁿ, the first linear, the other positive definite quadratic. Furthermore let Δ be a simplex contained in ℝⁿ (the set of admissible portfolios), for example Δ : x₁+ ... + xₙ = 1, $x_{i} \geq 0$ . Our goal is to investigate the properties of the restricted mappings (V,E):Δ → ℝ² (the so called Markowitz mappings) and to classify them. We introduce the notion of a...

Variance components estimation in generalized orthogonal models

Célia Fernandes, Paulo Ramos, Sandra Saraiva Ferreira, João Tiago Mexia (2007)

Discussiones Mathematicae Probability and Statistics

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The model $y = \sum_{j = 1}^{w} X_{j} β ̲_{j} + e ̲$ is generalized orthogonal if the orthogonal projection matrices on the range spaces of matrices $X_{j}$ , j = 1, ..., w, commute. Unbiased estimators are obtained for the variance components of such models with cross-nesting.