Comparisons of Some Weighting Methods for Non-response Adjustment

Abstract

Sample and population auxiliary information have been demonstrated to be useful and yield approximately equal resultsin large samples. Several functional forms of weights are suggested in the literature. This paper studies the properties of calibrationestimators when the functional form of response probability is assumed to be known. The focus is on the difference between populationand sample level auxiliary information, the latter being demonstrated to be more appropriate for estimating the coefficients in theresponse probability model. Results also suggest a two-step procedure, using sample information for model coefficient estimation inthe first step and calibration estimation of the study variable total in the second step.

Variance estimation in two-step calibration for nonresponse adjustment

“…Lehtonen and Veijanen, 2012;Lehtonen and Veijanen, 2015). Rota and Laitila (2015) combine LC and PC schemes and construct an alternative estimator of the total Y of a survey variable y by means of two-step estimation in the presence of sampleand population-level auxiliary information under the assumption of a known functional form of the response mechanism. In line with this setup, this paper contributes by deriving an approximate variance expression and suggesting a variance estimator for this alternative two-step estimator.…”

“…The two-step estimator suggested by Rota and Laitila (2015) assumes that the functional form of the response probability is known and is given by q k = q(z t k g).…”

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Rota and Laitila (2015) suggest an alternative two-step calibration estimation resulting from combining two calibration estimation approaches, i.e., linear calibration (Särndal and Lundström, 2005) and propensity score calibration (Chang and Kott, 2008), when the functional form of the response probability is assumed to be known. The first step focuses on estimating this function and the second step on estimating the total of a survey variable.

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A New Calibration Estimator of Population Mean for Small Area with Nonresponse

“…Though synthetic estimation technique has been adopted by different authors to compensate for the challenges of small sample sizes in SAE [2][3][4][5], with other contributors using calibration weights as a means of improving the precision, ( [6][7][8][9][10][11][12][13][14][15][16][17][18][19]), small or no sample size problem in the presence of unit nonresponse remains a gap in the literature.…”

Treating nonresponse in the estimation of the distribution function

“…Many different proposals for nonresponse weighting have been considered (see.eg. [1], [3], [9], [10], [11], [14], [17], [12]) in the estimation of linear parameters as total or mean, but lesser effort has been devoted in the development of efficient methods for estimating a population distribution. The distribution function is a relevant tool when the variable of interest is a measure of wages or income, since it is needed to calculate many poverty measures (the poverty line, the low income proportion, the poverty gap ...) For these reasons, estimation of the distribution function is an important issue in sample surveys that has received much attention in the last years.…”