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Contributions to Small Area Estimation: Using Random Effects Growth Curve Model
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
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: urn:nbn:se:liu:diva-137206DOI: 10.3384/diss.diva-137206ISBN: 9789176855164 (print)OAI: oai:DiVA.org:liu-137206DiVA, id: diva2:1094130
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
List of papers
1. Small Area Estimation under a Multivariate Linear Model for Repeated measures Data
Open this publication in new window or tab >>Small Area Estimation under a Multivariate Linear Model for Repeated measures Data
2017 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 21, p. 10835-10850Article in journal (Refereed) Published
Abstract [en]

In this article, Small Area Estimation under a Multivariate Linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points and per group units are derived. A parametric bootstrap method is proposed for estimating the mean squared error of the predicted small area means. Results are supported by a simulation study.

Place, publisher, year, edition, pages
New York: Taylor & Francis, 2017
National Category
Probability Theory and Statistics Control Engineering Applied Mechanics Geophysics
Identifiers
urn:nbn:se:liu:diva-137116 (URN)10.1080/03610926.2016.1248784 (DOI)000415766400033 ()
Note

Funding agencies: Swedish International Development and Cooperation Agency (SIDA); University of Rwanda; Swedish Foundation for Humanities and Social Sciences

Available from: 2017-05-05 Created: 2017-05-05 Last updated: 2017-12-13Bibliographically approved
2. Crop yield estimation at district level for agricultural seasons 2014 in Rwanda
Open this publication in new window or tab >>Crop yield estimation at district level for agricultural seasons 2014 in Rwanda
2016 (English)In: African Journal of Applied Statistics, ISSN 2316-0861, Vol. 3, no 1, p. 69-90Article in journal (Refereed) Published
Abstract [en]

In this paper, we discuss an application of Small Area Estimation (SAE) tech- niques under a multivariate linear regression model for repeated measures data to produce district level estimates of crop yield for beans which comprise two varieties, bush beans and climbing beans in Rwanda during agricultural seasons 2014. By using the micro data of National Institute of Statistics of Rwanda (NISR) obtained from the Seasonal Agricul- tural Survey (SAS) 2014 we derive efficient estimates which show considerable gain. The considered model and its estimates may be useful for policy-makers or for further analyses. 

National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-136721 (URN)10.16929/ajas/2016.69.203 (DOI)
Available from: 2017-04-21 Created: 2017-04-21 Last updated: 2017-05-09Bibliographically approved
3. Mean-squared errors of small area estimators under a multivariate linear model for repeated measures data
Open this publication in new window or tab >>Mean-squared errors of small area estimators under a multivariate linear model for repeated measures data
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
Mean-squared errors, Multivariate linear model, Repeated measures data, Small area estamation
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-137113 (URN)LiTH-MAT-R--2017/05--SE (ISRN)
Available from: 2017-05-05 Created: 2017-05-05 Last updated: 2017-11-02Bibliographically approved
4. Small area estimation under a multivariate linear model for incomplete repeated measures data
Open this publication in new window or tab >>Small area estimation under a multivariate linear model for incomplete repeated measures data
2017 (English)Report (Other academic)
Abstract [en]

In this paper, the issue of analysis of multivariate repeated measures data that follow a monotonic sample pattern for small area estimation is addressed. Random effects growth curve models with covariates for both complete and incomplete data are formulated. A conditional likelihood based approach is proposed for estimation of the mean parameters and covariances. Further, the prediction of random effects and predicted small area means are also discussed. The proposed techniques may be useful for small area estimation under longitudinal surveys with grouped response units and drop outs.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 12
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2017:06
Keywords
Conditional likelihood, Multivariate linear model, Monotone sample, Repeated measures data.
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-137118 (URN)LiTH-MAT-R--2017/06--SE (ISRN)
Available from: 2017-05-05 Created: 2017-05-05 Last updated: 2017-11-02Bibliographically approved

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