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Mean-squared errors of small area estimators under a multivariate linear model for repeated measures data
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Department of Mathematics, College of Science and Technology, University of Rwanda, Kigali, Rwanda.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden.ORCID iD: maroh70 0000-0001-9896-4438
2017 (English)Report (Other academic)
Abstract [en]

In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate the mean-squared errors (MSE) for the predicted small area means as a measure of precision. A two stage estimator of MSE is obtained. At the first stage, we derive the MSE when the covariance matrices are known. To obtain an unbiased estimator of the MSE, at the second stage, a method based on parametric bootstrap is  proposed for bias correction and for prediction error that reects the uncertainty when the unknown covariance is replaced by its suitable estimator.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. , p. 19
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2017:05
Keywords [en]
Mean-squared errors, Multivariate linear model, Repeated measures data, Small area estamation
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-137113ISRN: LiTH-MAT-R--2017/05--SELibris ID: 20807903OAI: oai:DiVA.org:liu-137113DiVA, id: diva2:1093289
Available from: 2017-05-05 Created: 2017-05-05 Last updated: 2017-11-02Bibliographically approved
In thesis
1. Contributions to Small Area Estimation: Using Random Effects Growth Curve Model
Open this publication in new window or tab >>Contributions to Small Area Estimation: Using Random Effects Growth Curve Model
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This dissertation considers Small Area Estimation with a main focus on estimation and prediction for repeated measures data. The demand of small area statistics is for both cross-sectional and repeated measures data. For instance, small area estimates for repeated measures data may be useful for public policy makers for different purposes such as funds allocation, new educational or health programs, etc, where decision makers might be interested in the trend of estimates for a specic characteristic of interest for a given category of the target population as a basis of their planning.

It has been shown that the multivariate approach for model-based methods in small area estimation may achieve substantial improvement over the usual univariate approach. In this work, we consider repeated surveys taken on the same subjects at different time points. The population from which a sample has been drawn is partitioned into several non-overlapping subpopulations and within all subpopulations there is the same number of group units. The aim is to propose a model that borrows strength across small areas and over time with a particular interest of growth profiles over time. The model accounts for repeated surveys, group individuals and random effects variations.

Firstly, a multivariate linear model for repeated measures data is formulated under small area estimation settings. The estimation of model parameters is discussed within a likelihood based approach, the prediction of random effects and the prediction of small area means across timepoints, per group units and for all time points are obtained. In particular, as an application of the proposed model, an empirical study is conducted to produce district level estimates of beans in Rwanda during agricultural seasons 2014 which comprise two varieties, bush beans and climbing beans.

Secondly, the thesis develops the properties of the proposed estimators and discusses the computation of their first and second moments. Through a method based on parametric bootstrap, these moments are used to estimate the mean-squared errors for the predicted small area means. Finally, a particular case of incomplete multivariate repeated measures data that follow a monotonic sample pattern for small area estimation is studied. By using a conditional likelihood based approach, the estimators of model parameters are derived. The prediction of random effects and predicted small area means are also produced.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 43
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1855
National Category
Probability Theory and Statistics Control Engineering Signal Processing Economics and Business Bioinformatics (Computational Biology)
Identifiers
urn:nbn:se:liu:diva-137206 (URN)10.3384/diss.diva-137206 (DOI)9789176855164 (ISBN)
Public defence
2017-06-08, Ada Lovelace (Visionen), B-huset, ingång 27, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2017-05-09 Created: 2017-05-09 Last updated: 2018-01-13Bibliographically approved

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