Combining Information from Multiple Surveys by using Regression for Efficient Small Domain Estimation

Abstract

In sample surveys of finite populations, subpopulations for which the sample size is too small for estimation of adequate precision are referred to as small domains. Demand for small domain estimates has been growing in recent years among users of survey data. We explore the possibility of enhancing the precision of domain estimators by combining comparable information collected in multiple surveys of the same population. For this, we propose a regression method of estimation that is essentially an extended calibration procedure whereby comparable domain estimates from the various surveys are calibrated to each other. We show through analytic results and an empirical study that this method may greatly improve the precision of domain estimators for the variables that are common to these surveys, as these estimators make effective use of increased sample size for the common survey items. The design-based direct estimators proposed involve only domain-specific data on the variables of interest. This is in contrast with small domain (mostly small area) indirect estimators, based on a single survey, which incorporate through modelling data that are external to the targeted small domains. The approach proposed is also highly effective in handling the closely related problem of estimation for rare population characteristics. Copyright (c) 2010 Royal Statistical Society.

Empirical Likelihood Approach for Aligning Information from Multiple Surveys

“…'), based on adjustment factors. In this simulation study, we use the adjustment factor n t (1− n t N −1 ) −1 (Merkouris, , Section 3.1). In Section , we show that the proposed empirical likelihood approach should not be affected by small sample sizes.…”

“…In particular, a choice that minimises the estimated variance yields and optimal estimator (e.g. Merkouris, ; ). This, however, requires variance estimation and may be difficult for complex sampling designs.…”

Combining Data from New and Traditional Sources in Population Surveys

“…It is envisaged that for reasons of confidentiality, users might receive only the Survey A synthetic data sets and replicate weights. Merkouris (2010Merkouris ( , 2013 developed a framework for a single population with multivariate response variable, which includes as special cases (i) samples from separate surveys, (ii) a split sample of a single survey, (iii) multiple samples of a single survey and (iv) nested samples of a single survey. If the number of samples is m, and k i estimates are available for total Y i , 1 Ä k i Ä m, the problem is to find for each Y i the 'best' linear composite estimator combining the information from the m different samples.…”

A global optimisation approach to range-restricted survey calibration

“…A compact form for the asymptotic variance of the generalised regression estimator can be found e.g. in Merkouris (2010). Alternative jackknife estimates of variance can be used in a more general context and were shown to outperform Taylorbased techniques for estimating the variance of calibration estimators in Stukel et al (1996).…”

“…Survey calibration at the domain level and/or knowledge on the domain size, or combining information from multiple surveys at the domain level, provides approximately unbiased design-consistent estimators with substantial variance reduction with respect to other estimators (Merkouris 2010). An intermediate option is adopted in small area estimation (by, for example, but not limited to, spatial microsimulation) when (sufficient) survey data are not available for a small area, consisting in using outof-area survey data in combination with known area totals (Tanton 2014).…”