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1

On mse estimators of eblup of domain total under some longitudinal model

100%

Żądło T.

Mathematical Economics

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2013

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issue 9 (16)

117-127

EN

Żądło (2012) proposed a certain unit-level longitudinal model which was a special case of the General Linear Mixed Model. Two vectors of random components included in the model obey assumptions of simultaneous spatial autoregressive process (SAR) and temporal first-order autoregressive process (AR(1)) respectively. Moreover, it is assumed that the population can change in time and the population elements can change its domains’ (subpopulations’) affiliation in time. Under the proposed model, Żądło (2012) derived the Empirical Best Linear Unbiased Predictor (EBLUP) of the domain total. What is more (based on the theorem proved by Żądło (2009)), the approximate equation of the mean squared error (MSE) was derived and its estimator based on the Taylor approximation was proposed. The proposed MSE estimator was derived under some assumptions including that the variance-covariance matrix can be decomposed into linear combination of variance components. The assumption was not met under the proposed model. In the paper the jackknife MSE estimator for the derived EBLUP will be proposed based on the results presented by Jiang, Lahiri, Wan (2002). The bias of the jackknife MSE estimator will be compared in the simulation study with the bias of the MSE estimator based on the Taylor approximation.

2

On MSE Estimation of Some Misspecified Predictor

100%

Żądło T., University of Economics in Katowice D. o. S.

Acta Universitatis Lodziensis. Folia Oeconomica

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2013

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vol. 286

EN

The problem of prediction of subpopulation (domain) total is studied as in Rao (2003). The problem is inspired by results obtained by Żądło (2012) who considered two predictors – empirical best linear unbiased predictor (EBLUP) under some correct model and some simpler misspecified predictor. In the simulation study he showed that the misspecified predictor may be in some cases more accurate than the EBLUP derived under the correct model what resulted from the decrease of accuracy of the EBLUP due to the estimation of unknown parameters of the correct model. But the problem occurred in the case of MSE estimation – under the correct model the bias of the MSE estimator derived under the misspecified model was very large. Hence, in the paper we consider a predictor based on some misspecified model and we derive some MSE estimator under the correct model and we propose usage of two other MSE estimators.

PL

Rozważany jest problem predykcji wartości globalnej w podpopulacji (domenie) jak w Rao (2003). Analizowane jest wykorzystanie predyktora, który jest empirycznym najlepszym liniowym nieobciążonym predyktorem, ale przy założeniu błędnego modelu. Dla rozważanego predyktora wyprowadzono postać naiwnego estymatora MSE dla prawidłowego modelu nadpopulacji oraz zaproponowano wykorzystanie estymatorów MSE typu jackknife i parametryczny bootstrap. W badaniu symulacyjnym analizowano względne obciążenia zaproponowanych estymatorów MSE.

3

On the generalisation of Quatember's bootstrap

100%

Żądło T.

Statistics in Transition new series

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2021

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vol. 22

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issue 1

163-178

EN

The problem of the estimation of the design-variance and the design-MSE of different estimators and predictors is considered. Bootstrap algorithms applicable to complex sampling designs are used. A generalisation of the bootstrap procedure studied by Quatember (2014) is proposed. In most of the cases considered in our simulation study it leads to more accurate estimates (or to very similar ones in remaining cases) of the designMSE and the design-variance compared with the original algorithm and its other counteparts.

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1 Acta Universitatis Lodziensis. Folia Oeconomica

1 Mathematical Economics

1 Statistics in Transition new series

3 Żądło T.

1 University of Economics in Katowice D. o. S.

1 2021

2 2013

On mse estimators of eblup of domain total under some longitudinal model

On MSE Estimation of Some Misspecified Predictor

On the generalisation of Quatember's bootstrap