Locally and uniformly best estimators in replicated regression model

Júlia Volaufová; Lubomír Kubáček

Displaying similar documents to “Locally and uniformly best estimators in replicated regression model”

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.

Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study

A. K. Md. Ehsanes Saleh, Radim Navrátil (2018)

Kybernetika

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In the development of efficient predictive models, the key is to identify suitable predictors for a given linear model. For the first time, this paper provides a comparative study of ridge regression, LASSO, preliminary test and Stein-type estimators based on the theory of rank statistics. Under the orthonormal design matrix of a given linear model, we find that the rank based ridge estimator outperforms the usual rank estimator, restricted R-estimator, rank-based LASSO, preliminary...

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

Arkadiusz Kozioł (2016)

Discussiones Mathematicae Probability and Statistics

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In this article author obtain the best unbiased estimators of doubly exchangeable covariance structure. For this purpose the coordinate free-coordinate approach is used. Considered covariance structure consist of three unstructured covariance matrices for three-level $m -$ variate observations with equal mean vector over v points in time and u sites under the assumption of multivariate normality. To prove, that the estimators are best unbiased, complete statistics are used. Additionally,...

The linear model with variance-covariance components and jackknife estimation

Jaromír Kudeláš (1994)

Applications of Mathematics

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Let $θ^{*}$ be a biased estimate of the parameter $ϑ$ based on all observations $x_{1}$ , $\dots$ , $x_{n}$ and let $θ_{- i}^{*}$ ( $i = 1, 2, \dots, n$ ) be the same estimate of the parameter $ϑ$ obtained after deletion of the $i$ -th observation. If the expectation of the estimators $θ^{*}$ and $θ_{- i}^{*}$ are expressed as $\begin{matrix} E (θ^{*}) & = ϑ + a (n) b (ϑ) \\ E (θ_{- i}^{*}) & = ϑ + a (n - 1) b (ϑ) i = 1, 2, \dots, n, \end{matrix}$ where $a (n)$ is a known sequence of real numbers and $b (ϑ)$ is a function of $ϑ$ , then this system of equations can be regarded as a linear model. The least squares method gives the generalized jackknife estimator. Using this method, it is possible to obtain...