On the calibration of design weights using a displacement function

Abstract

In the present investigation, we propose a new method to calibrate the estimator of the general parameter of interest in survey sampling. We demonstrate that the linear regression estimator due to Hansen et al. (Sample Survey Method and Theory. Wiley, NY, 1953) is a special case of this. We reconfirm that the sum of calibrated weights has to be set equal to sum of the design weights within a given sample as shown in Singh (Advanced sampling theory with applications: How Michael ‘selected’ Amy, Vol. 1 and 2. Kluwer, The Netherlands, pp 1–1247, 2003; Proceedings of the American Statistical Association, Survey Method Section [CD-ROM], Toronto, Canada: American Statistical Association, pp 4382–4389, 2004; Metrika:1–18, 2006a; Presented at INTERFACE 2006, Pasadena, CA, USA, 2006b) and Stearns and Singh (Presented at Joint Statistical Meeting, MN, USA (Available on the CD), 2005; Comput Stat Data Anal 52:4253–4271, 2008). Thus, it shows that the Sir. R.A. Fisher’s brilliant idea of keeping sum of observed frequencies equal to that of expected frequencies leads to a “Honest-Balance” while weighing design weights in survey sampling. The major benefit of the proposed new estimator is that it always works unlike the pseudo empirical likelihood estimators listed in Owen (Empirical Likelihood. Chapman & Hall, London, 2001), Chen and Sitter (Stat Sin 9:385–406, 1999) and Wu (Sur Methodol 31(2):239–243, 2005). The main endeavor of this paper is to bring a change in the existing calibration technology, which is based on only positive distance functions, with a displacement function that has the flexibility of taking positive, negative, or zero value. At the end, the proposed technology has been compared with its competitors under several kinds of linear and non-linear non-parametric models using an extensive simulation study. A couple of open questions are raised.