Small area estimation under unit-level temporal linear mixed models

ABSTRACT

Data from past time periods and temporal correlation are rich sources of information for estimating small area parameters at the current period. This paper investigates the use of unit-level temporal linear mixed models for estimating linear parameters. Two models are considered, with domain and domain-time random effects. The first model assumes time independency and the second one AR(1)-type time correlation. They are fitted by a Fisher-scoring algorithm that calculates the residual maximum likelihood estimators of the model parameters. Based on the introduced models, empirical best linear unbiased predictors of small area linear parameters are studied, and analytic estimators for evaluating the performance of their mean squared errors are proposed. Three simulation experiments are carried out to study the behaviour of the fitting algorithm, the small area predictors and the estimators of the mean squared error. By using data of the Spanish surveys of income and living conditions of 2004–2008, an application to the estimation of 2008 average normalized net annual incomes in Spanish provinces by sex is given.

Keywords:

• Small area estimation
• linear mixed models
• empirical best linear unbiased predictor
• mean squared error
• average income

Mathematics Subject Classifications:

• 62J12 generalized linear models
• 62P25 applicationsto social sciences
• 62D05 sampling theory
• sample surveys

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by the Spanish grant MTM2015-64842-P from Ministerio de Economía y Competitividad.