Carl-Erik Särndal

Calibration Estimators in Survey Sampling

Abstract This article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information. Estimation is equivalent to attaching weights to the survey data. We focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations. We briefly mention an application to the case in which the information consists of known marginal counts in a two- or multi-way table, known as generalized raking. The general regression estimator (GREG) was conceived with multivariate auxiliary information in mind. Ordinarily, this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x. But we note that the GREG can be derived by a different route by focusing instead on the weights. The ordinary sampling weights of the kth observation is 1/πk , where πk is the inclusion probabilit...

Generalized Raking Procedures in Survey Sampling

Abstract We propose the name generalized raking for the class of procedures developed in this article, because the classical raking ratio of W. E. Deming is a special case. Generalized raking can be used for estimation in surveys with auxiliary information in the form of known marginal counts in a frequency table in two or more dimensions. An important property of the generalized raking weights is that they reproduce the known marginal counts when applied to the categorical variables that define the frequency table. Our starting point is a class of distance measures and a set of original weights in the form of the standard sampling weights 1/π k , where π k is the inclusion probability of element k. New weights are derived by minimizing the total distance between original weights and new weights. The article makes contributions in three areas: (1) statistical inference conditionally on estimated cell counts, (2) simple calculation of variance estimates for the generalized raking estimators, and (3) presen...

Small Domain Estimation: A Conditional Analysis

Abstract In estimating means, totals, and other parameters for small domains of a finite population, the survey statistician is usually faced with a domain sample size that is random rather than controlled at the selection stage. Often a sensible approach is to make design-based inference conditionally on the realized sample size in the domain (nd ). In this article, we suggest and analyze some small domain estimators and their design-based conditional confidence intervals. The conditional outlook leads us to some new small domain estimators that (a) are based on regression of pertinent auxiliary information and are therefore efficient to the extent that the auxiliary information is strong; (b) are nearly design unbiased, conditionally on nd , as well as unconditionally; and (c) give rise to design-based confidence intervals that are valid conditionally as well as unconditionally. The conditional properties of these new regression estimators are first derived theoretically, then confirmed through a Monte ...

Efficient Estimators with Simple Variance in Unequal Probability Sampling

Abstract For unequal probability sampling designs, design-based variance estimation is cumbersome because it requires second-order inclusion probabilities. For most fixed sample size probability proportional-to-size (φPS) schemes, these probabilities are difficult to compute, and the variance estimation depends on them for a tedious double-sum calculation. We show how to replace the traditional φPS scenario with simpler design/estimator alternatives that preserve the high efficiency characteristic of φPS schemes. These use the generalized regression estimator, and the variance estimation entails only the calculation of a simple weighted squared residual sum.

Aspects of Responsive Design with Applications to the Swedish Living Conditions Survey

Abstract In recent literature on survey nonresponse, new indicators of the quality of the data collection have been proposed. These include indicators of balance and representativity (of the set of respondents) and distance (between respondents and nonrespondents), computed on available auxiliary variables. We use such indicators in conjunction with paradata from the Swedish CATI system to examine the inflow of data (as a function of the call attempt number) for the 2009 Swedish Living Conditions Survey (LCS). We then use the LCS 2009 data file to conduct several “experiments in retrospect”. They consist in interventions, at suitable chosen points and driven by the prospects of improved balance and reduced distance. The survey estimates computed on the resulting final response set are likely to be less biased. Cost savings realized by fewer calls can be redirected to enhance quality of other aspects of the survey design.

A two‐way classification of regression estimation strategies in probability sampling

This paper examines strategies for estimating the mean of a finite population in the following situation: A linear regression model is assumed to describe the population scatter. Various estimators β for the vector of regression parameters β are considered. Several ways of transforming each estimator β into a model-based estimator for the population mean are considered. Some estimators constructed in this way become sensitive to correctness of the assumed model. The estimators favoured in this paper are the ones in which the observations are weighted to reflect the sampling design, so that asymptotic design unbiasedness is achieved. For these estimators, the randomization distribution gives protection against model breakdown.

Inconsistent Regression and Nonresponse Bias: Exploring Their Relationship as a Function of Response Imbalance

Abstract One objective of adaptive data collection is to secure a better balanced survey response. Methods exist for this purpose, including balancing with respect to selected auxiliary variables. Such variables are also used at the estimation stage for (calibrated) nonresponse weighting adjustment. Earlier research has shown that the use of auxiliary information at the estimation stage can reduce bias, perhaps considerably, but without eliminating it. The question is: would it have contributed further to bias reduction if, prior to estimation, that information had also been used in data collection, to secure a more balanced set of respondents? If the answer is yes, there is clear incentive, from the point of view of better accuracy in the estimates, to practice adaptive survey design, otherwise perhaps not. A key question is how the regression relationship between the survey variable and the auxiliary vector presents itself in the sample as opposed to the response. Strength in the relationship is helpful but is not the only consideration. The dilemma with nonresponse is one of inconsistent regression: a regression model appropriate for the sample often fails for the responding subset, because nonresponse is selective, non-random. In this article, we examine how nonresponse bias in survey estimates depends on regression inconsistency, both seen as functions of response imbalance. As a measure of bias we use the deviation of the calibration adjusted estimator from the unbiased estimate under full response. We study how the deviation and the regression inconsistency depend on the imbalance. We observe in empirical work that both can be reduced, to a degree, by efforts to reduce imbalance by an adaptive data collection.