Multivariate structure preserving estimation for population compositions

Abstract

This document introduces a new Structure Preserving Estimator for Small Area compositions, using data from a proxy and a sample compositions. The proposed estimator, the Multivariate Structure Preserving Estimator (MSPREE), extends the two main SPREE-type estimators: the SPREE and the GSPREE. The additional flexibility of the MSPREE may lead to estimates with less MSE than its predecessors. An extension of the MSPREE including cell specific random effects, the Mixed MSPREE (MMSPREE), is also presented, in an attempt to further reduce the size of the bias when the associated sample size allows for it. In order to estimate the variance components governing the variance structure of the random effects in the MMSPREE, an unbiased moment-type estimator is proposed. Furthermore, an estimator for the variance of the MSPREE, as well as methodologies to evaluate the unconditional and finite population MSE of both MSPREE and MMSPREE, are developed. The behaviour of the proposed estimators is illustrated in a controlled setting via a simulation exercise, and in a real data application.

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Identifiers

ORCID for Nikos Tzavidis: orcid.org/0000-0002-8413-8095

ORCID for Li-Chun Zhang: orcid.org/0000-0002-3944-9484

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