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A common problem is to compare two cross-sectional estimates for the same study variable taken on two different waves or occasions, and to judge whether the change observed is statistically significant. This involves the estimation of the sampling variance of the estimator of change. The estimation of this variance would be relatively straightforward if cross-sectional estimates were based on the same sample. Unfortunately, samples are not completely overlapping, because of rotations used in repeated surveys. We propose a simple approach based on a multivariate (general) linear regression model. The variance estimator proposed is not a model-based estimator. We show that the estimator proposed is design consistent when the sampling fractions are negligible. It can accommodate stratified and two-stage sampling designs. The main advantage of the approach proposed is its simplicity and flexibility. It can be applied to a wide class of sampling designs and can be implemented with standard statistical regression techniques. Because of its flexibility, the approach proposed is well suited for the estimation of variance for the European Union Statistics on Income and Living Conditions surveys. It allows us to use a common approach for variance estimation for the different types of design. The approach proposed is a useful tool, because it involves only modelling skills and requires limited knowledge of survey sampling theory.

A common problem in survey sampling is to compare two cross-sectional estimates for the same study variable taken on two different waves or occasions. These cross-sectional estimates often include imputed values to compensate for item non-response. The estimation of the sampling variance of the estimator of change is useful to judge whether the observed change is statistically significant. Estimating the variance of a change is not straightforward due to rotation in repeated surveys. We propose using a multivariate linear regression approach and show how it can be used to accommodate the effect of imputation. The regression approach gives design-consistent estimation of the variance of change when the sampling fraction is small. We illustrate the proposed approach using random hot-deck imputation, although the proposed estimator can be implemented with other imputation techniques.

Interpreting changes between point estimates at different waves may be misleading, if we do not take the sampling variation into account. It is therefore necessary to estimate the standard error of these changes in order to judge whether or not the observed changes are statistically significant. This involves the estimation of temporal correlations between cross sectional estimates, because correlations play an important role in estimating the variance of change in the cross-sectional estimates. Standard estimator for correlations cannot be used, because of the rotation used in most panel surveys, such as the European Union Statistics on Income and Living Conditions (EU-SILC) surveys. Furthermore, as poverty indicators are complex functions of the data, they need a special treatment when estimating their variance. For example, poverty rates depend on poverty thresholds which are estimated from medians. We propose to use a multivariate linear regression approach to estimate correlations by taking into account of the variability of the poverty threshold. We apply the proposed approach to the Turkish EU-SILC survey data.

Longitudinal surveys collect information on several occasions , or time points. Consider that we have two occasions or waves labelled 1 and 2. The samples selected on occasions 1 and 2 are rarely completely overlapping samples, as not all the units are selected on both occasions. It is common practice to have a large fraction of units sampled at both occasions. Surveys which have this feature are called rotating sampling surveys. The customary point estimators are the Horvitz Thompson and generalised regression estimators of a total or a mean. We propose a new regression estimator for cross-sectional totals and change between totals. This estimator uses the information from both occasions simultaneously instead of each occasion separately. This estimator incorporates the auxiliary variables similar to the general regression estimator and the sample design variables specifying the rotating sampling design. The proposed estimator is multivariate because it combines the auxiliary information from the first and second occasion. Longitudinal surveys are used to monitor change between population target parameters. For social policy makers, the estimation of change over time of social indicators as such youth employment rate, literacy rate and social deprivation indicators may be as important as cross-sectional indicators. The variance of change, for rotating sampling surveys, is a challenging subject since it requires to estimate correlations. Several authors proposed different estimators for correlations. A variance of change is proposed by extending the estimator proposed Berger & Priam (2015) where besides the design variables, the auxiliary variables are included. In the simulation study, the proposed estimator is compared with the Horvitz Thompson (HT) and generalised regression estimators. The relative bias and ratio of relative mean square errors are computed for the estimator of totals. We consider different correlations between the response variables and the auxiliary variables

The approach proposed gives design-consistent estimators of parameters which are solutions of estimating equations (e.g. averages, totals, quantiles, correlation, (non)linear regression parameters). It can be used to construct confidence intervals without variance estimates. These confidence intervals are not based on the normality of the point estimator. Linearisation, re-sampling (jackknife or bootstrap) or joint-inclusion probabilities are not necessary, even when the parameter of interest is not linear. This approach gives consistent confidence intervals even when the sampling distribution is skewed (e.g. with domains or with outlying values), or when linearisation gives biased variance estimates. The proposed approach can be used to estimate generalised regression parameters (e.g. logistic regression) and to test if they are significant, under a design-based approach. The auxiliary information is naturally taken into account, without the need of a calibration distance function. The empirical likelihood approach is a design-based approach. A super-population model is not necessary. The empirical likelihood approach proposed is different from the pseudoempirical likelihood approach

The Hartley-Rao-Cochran (RHC) sampling design (Rao et al., 1962) is a popular unequal probability sampling design. We show how empirical likelihood confidence intervals can be derived under this sampling design. Berger and De La Riva Torres (2012) proposed an empirical likelihood approach which can be used for point estimation and to construct confidence intervals under complex sampling designs. We show how this approach can be adjusted for the RHC sampling design. The proposed approach intrinsically incorporates sampling weights and auxiliary information. It may give better coverages than standard methods even when the sampling distribution of the parameters of interest is not normal. The proposed approach is simple to implement and less computer intensive than bootstrap. The proposed approach does not rely on re-sampling, linearisation, variance estimation, or design-effects.

The paper presents the current state of progress of the Net-SILC2 work package dealing with standard error estimation and other related sampling issues in EU-SILC. The aim of this work package is to develop a practicable set of recommendations on standard error estimation both for data producers (NSIs) and data users. The increased complexity of EU-SILC, the widening of the user community and the increased reliance on EU-SILC for policy targeting and evaluation, particularly since the launch of the "Europe 2020" Strategy for smart, sustainable and inclusive growth, have enhanced the need for comparable, accurate as well as workable solutions for the estimation of standard errors and confidence intervals. After presenting the variance estimation methodology that has been proposed, the paper shows preliminary results for cross-sectional and longitudinal measures and for measures of net change.

We present the first results of the Net-SILC2 project with regard to standard error estimation in EU-SILC (EU Statistics on Income and Living Conditions). EU-SILC is the main data source for comparative analysis and indicators on income and living conditions in the European Union (EU), covering all the 27 EU countries and a number of other European countries. The growing complexity of EU-SILC, the widening of the user community and the increasing reliance on EU-SILC for policy targeting and evaluation have enhanced the need for comparable, accurate as well as workable solutions to the estimation of standard errors and confidence intervals for the indicators based on the EU-SILC surveys. After presenting the Net-SILC2 project and the recommended variance estimators, we show preliminary estimates of standard error and confidence intervals for cross-sectional measures, longitudinal measures and measures of changes between two waves. The proposed approach is general and can be implemented with multistage surveys. As far as variance of change is concerned, the proposed approach can be used with rotating longitudinal surveys (Kalton 2009) such as Labour Force Surveys

A large part of survey sampling literature is devoted to unequal probabilities sampling designs without replacement. Brewer and Hanif (1983) provided a summary of these sampling designs. The maximum entropy designs is one of them. Consistency results have been proven for the maximum entropy sampling (Hájek, 1964). The aim is to give sufficient conditions under which Hájek (1964) consistency results still hold for large entropy sampling designs which are different from the maximum entropy design. These conditions involve modes of convergence of sampling designs towards the maximum entropy design. We show that these conditions are satisfied for the popular Rao-Sampford (Rao, 1965, Sampford, 1967) design. Our consistency results are applied to the Hájek (1964) simple variance estimator. This estimator does not require joint-inclusion probabilities and can be easily estimated using weighted least squares regression (Berger, 2004, 2005b). Deville (1999) conjectured that this estimator is suitable for any sampling designs (see also Brewer and Donadio, 2003). Our consistency result gives regularity conditions under which this estimator is consistent which justifies Deville’s (1999) conjecture.

Estimation of quantiles may be of considerable interest when measuring income distribution and poverty lines. For instance, the median is regarded as a more appropriate measure of location than the mean when variables, such as income, expenditure, etc, exhibit highly skewed distributions. In sample surveys, auxiliary information is often used at the estimation stage to increase the precision of estimators of means. The use of auxiliary information has been studied extensively for estimation of means, but it has no obvious extensions to the estimation of quantiles. A novel method for estimating quantiles using auxiliary information is proposed. The proposed estimator is based upon the regression estimator of a transformed variable of interest. Simulation studies support our findings and show that the proposed estimator can be more accurate than or as accurate as alternative estimators (Chambers & Dunstan, 1986; Rao et al. 1990; Silva & Skinner 1995) which can be computationally more intensive.

The Gini coefficient (Gini 1914) has proved valuable as a measure of income inequality. In cross-sectional studies of the Gini coefficient, information about the accuracy of its estimates is crucial. We show how to use jackknife and linearization to estimate the variance of the Gini coefficient, allowing for the effect of the sampling design. The aim is to show the asymptotic equivalence (or consistency) of the generalized jackknife estimator (Campbell 1980) and the Taylor linearization estimator (Kovac?evic´ and Binder 1997) for the variance of the Gini coefficient. A brief simulation study supports our findings

Survey sampling textbooks often refer to the Sen-Yates-Grundy variance estimator for use with without replacement unequal probability designs. This estimator is rarely implemented, because of the complexity of determining joint inclusion probabilities. In practice, the variance is usually estimated by simpler variance estimators such as the Hansen-Hurwitz with replacement variance estimator; which often leads to overestimation of the variance for large sampling fraction that are common in business surveys. We will consider an alternative estimator: the Hájek (1964) variance estimator that depends on the first-order inclusion probabilities only and is usually more accurate than the Hansen-Hurwitz estimator. We review this estimator and show its practical value. We propose a simple alternative expression; which is as simple as the Hansen-Hurwitz estimator. We also show how the Hájek estimator can be easily implemented with standard statistical packages.

We propose to estimate the design variance of absolute changes between two cross-sectional estimators under rotating sampling schemes. We show that the variance estimator proposed is generally positive. We also propose possible extensions for stratified samples, with dynamic stratification; that is, when units move between strata and new strata are created at the second waves.

Proportions below a given fraction of a quantile of an income distribution are often estimated from survey data in poverty comparisons. We consider the estimation of the variance of such a proportion, estimated from Family Expenditure Survey data. We show how a linearization method of variance estimation may be applied to this proportion, allowing for the effects of both a complex sampling design and weighting by a raking method to population controls. We show that, for 1998-99 data, the estimated variances are always increased when allowance is made for the design and raking weights, the principal effect arising from the design. We also study the properties of a simplified variance estimator and discuss extensions to a wider class of poverty measures.