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A sufficient condition for admissibility in linear estimation

Czesław Stępniak (1988)

Aplikace matematiky

It was recently shown that all estimators which are locally best in the relative interior of the parameter set, together with their limits constitute a complete class in linear estimation, both unbiased and biased. However, not all these limits are admissible. A sufficient condition for admissibility of a limit was given by the author (1986) for the case of unbiased estimation in a linear model with the natural parameter space. This paper extends this result to the general linear model and to biased...

Adaptive trimmed likelihood estimation in regression

Tadeusz Bednarski, Brenton R. Clarke, Daniel Schubert (2010)

Discussiones Mathematicae Probability and Statistics

In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent robust...

Additional Experiment and Linear Statistical Models

Lubomír Kubáček (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

An accuracy of parameter estimates need not be sufficient for their unforeseen utilization. Therefore some additional measurement is necessary in order to attain the required precision. The problem is to express the correction to the original estimates in an explicit form.

Admissible invariant estimators in a linear model

Czesław Stępniak (2014)

Kybernetika

Let 𝐲 be observation vector in the usual linear model with expectation 𝐀 β and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic 𝐚 T 𝐲 is called invariant estimator for a parametric function φ = 𝐜 T β if its MSE depends on β only through φ . It is shown that 𝐚 T 𝐲 is admissible invariant for φ , if and only if, it is a BLUE of φ , in the case when φ is estimable with zero variance, and it is of the form k φ ^ , where k ∈ 0 , 1 and φ ^ is an arbitrary BLUE, otherwise. This result is used in...

Aligned rank tests in measurement error model

Radim Navrátil, A. K. Md. Ehsanes Saleh (2016)

Applications of Mathematics

Aligned rank tests are introduced in the linear regression model with possible measurement errors. Unknown nuisance parameters are estimated first and then classical rank tests are applied on the residuals. Two situations are discussed: testing about an intercept in the linear regression model considering the slope parameter as nuisance and testing of parallelism of several regression lines, i.e. whether the slope parameters of all lines are equal. Theoretical results are derived and the simulation...

All about the ⊥ with its applications in the linear statistical models

Augustyn Markiewicz, Simo Puntanen (2015)

Open Mathematics

For an n x m real matrix A the matrix A⊥ is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of references

An adaptive method of estimation and outlier detection in regression applicable for small to moderate sample sizes

Brenton R. Clarke (2000)

Discussiones Mathematicae Probability and Statistics

In small to moderate sample sizes it is important to make use of all the data when there are no outliers, for reasons of efficiency. It is equally important to guard against the possibility that there may be single or multiple outliers which can have disastrous effects on normal theory least squares estimation and inference. The purpose of this paper is to describe and illustrate the use of an adaptive regression estimation algorithm which can be used to highlight outliers, either single or multiple...

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