Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure and structured mean vector

Arkadiusz Kozioł

Displaying similar documents to “Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure and structured mean vector”

Locally and uniformly best estimators in replicated regression model

Júlia Volaufová, Lubomír Kubáček (1983)

Aplikace matematiky

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The aim of the paper is to estimate a function $γ = t r (D β β^{'}) + t r (C \sum)$ (with $d, C$ known matrices) in a regression model $(Y, X β, \sum)$ with an unknown parameter $β$ and covariance matrix $\sum$ . Stochastically independent replications $Y_{1}, ..., Y_{m}$ of the stochastic vector $Y$ are considered, where the estimators of $X β$ and $\sum$ are $\bar{Y} = \frac{1}{m} \sum_{i = 1}^{m} Y_{i}$ and $\sum^{^} = {(m - 1)}^{- 1} \sum_{i = 1}^{m} (Y_{i} - \bar{Y}) {(Y_{i} - \bar{Y})}^{'}$ , respectively. Locally and uniformly best inbiased estimators of the function $γ$ , based on $\bar{Y}$ and $\sum^{^}$ , are given.

Bayes unbiased estimators of parameters of linear trend with autoregressive errors

František Štulajter (1987)

Aplikace matematiky

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The method of least wquares is usually used in a linear regression model $𝐘 = 𝐗 β + ϵ$ for estimating unknown parameters $β$ . The case when $ϵ$ is an autoregressive process of the first order and the matrix $𝐗$ corresponds to a linear trend is studied and the Bayes approach is used for estimating the parameters $β$ . Unbiased Bayes estimators are derived for the case of a small number of observations. These estimators are compared with the locally best unbiased ones and with the usual least squares estimators. ...

Estimation of a quadratic function of the parameter of the mean in a linear model

Júlia Volaufová, Peter Volauf (1989)

Aplikace matematiky

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The paper deals with an optimal estimation of the quadratic function $β^{'} 𝐃 β$ , where $β \in ℛ^{k}, 𝐃$ is a known $k \times k$ matrix, in the model $𝐘, 𝐗 β, σ^{2} 𝐈$ . The distribution of $𝐘$ is assumed to be symmetric and to have a finite fourth moment. An explicit form of the best unbiased estimator is given for a special case of the matrix $𝐗$ .

Asymptotic properties of the growth curve model with covariance components

Ivan Žežula (1997)

Applications of Mathematics

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We consider a multivariate regression (growth curve) model of the form $Y = X B Z + ε$ , $E ε = 0$ , $var (vec ε) = W \otimes Σ$ , where $W = \sum_{i = 1}^{k} θ_{i} V_{i}$ and $θ_{i}$ ’s are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters ${B_{i j}}$ estimating simultaneously the first and the second order parameters.

Bayesian and generalized confidence intervals on variance ratio and on the variance component in mixed linear models

Andrzej Michalski (2009)

Discussiones Mathematicae Probability and Statistics

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The paper deals with construction of exact confidence intervals for the variance component σ₁² and ratio θ of variance components σ₁² and σ² in mixed linear models for the family of normal distributions $_{t} (0, σ ₁ ² W + σ ² I_{t})$ . This problem essentially depends on algebraic structure of the covariance matrix W (see Gnot and Michalski, 1994, Michalski and Zmyślony, 1996). In the paper we give two classes of bayesian interval estimators depending on a prior distribution on (σ₁², σ²) for: 1) the variance components...