The linear model with variance-covariance components and jackknife estimation

Jaromír Kudeláš

Displaying similar documents to “The linear model with variance-covariance components and jackknife estimation”

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 $𝐗$ .

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.