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Liu-type shrinkage estimations in linear models

Yüzbaşı, Bahadır ; Asar, Yasin ; Ahmed, S. Ejaz

Statistics (Berlin, DDR), 2022-03, Vol.56 (2), p.396-420 [Periódico revisado por pares]

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Título:
Liu-type shrinkage estimations in linear models
Autor: Yüzbaşı, Bahadır ; Asar, Yasin ; Ahmed, S. Ejaz
Assuntos: Estimators ; full model ; Monte Carlo simulation ; penalty estimation ; pretest and shrinkage estimation ; Sub-model
É parte de: Statistics (Berlin, DDR), 2022-03, Vol.56 (2), p.396-420
Descrição: In this study, we present the preliminary test, Stein-type and positive part Stein-type Liu estimators in the linear models when the parameter vector $ {\boldsymbol {\beta }} $ β is partitioned into two parts, namely, the main effects $ {\boldsymbol {\beta }}_1 $ β 1 and the nuisance effects $ {\boldsymbol {\beta }}_2 $ β 2 such that $ {\boldsymbol {\beta }}=\left ({\boldsymbol {\beta }}_1, {\boldsymbol {\beta }}_2 \right ) $ β = ( β 1 , β 2 ) . We consider the case that a priori known or suspected set of the explanatory variables do not contribute to predict the response so that a sub-model may be enough for this purpose. Thus, the main interest is to estimate $ {\boldsymbol {\beta }}_1 $ β 1 when $ {\boldsymbol {\beta }}_2 $ β 2 is close to zero. Therefore, we investigate the performance of the suggested estimators asymptotically and via a Monte Carlo simulation study. Moreover, we present a real data example to evaluate the relative efficiency of the suggested estimators, where we demonstrate the superiority of the proposed estimators.
Editor: Abingdon: Taylor & Francis
Idioma: Inglês

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