The generalized exponential model for sampling weight calibration for extreme values, nonresponse, and poststratification
Folsom, R. E., & Singh, A. C. (2000). The generalized exponential model for sampling weight calibration for extreme values, nonresponse, and poststratification. In American Statistical Association, pp. 598–603. .
Consider a finite population U from which a sample of size n is selected using the design p(s). Denote the data by (Yk, Xk, dk), k ~ s, where for the k th unit in the sample, Yk is the study variable, Xk is a p-vector of covariates or predictor variables; and dk is the design weight. In practice, the d-weights are often adjusted to get the final w-weights in view of the triple concerns of (i) variance inflation of small domain estimates due to extreme values, (ii) bias due to nonresponse (nr), and (iii) bias due to under/over coverage. For the first one, winsorization (i.e., trimming part of the weight beyond the boundary defining extreme values) is often used to adjust extreme values but this may lose its impact after adjustments for nr and coverage; for the second one, weights are adjusted by the inverse response propensity factor (this is typically implemented by calibrating respondent weights to (random) control totals for covariates in the nr model obtained from the full sample of respondents and nonrespondents ) but in the process some weights could become extreme; and for the third one, weights are adjusted by poststratification (ps) (this is typically realized by calibrating weights to nonrandom controls for covariates in the ps model) but in the process some of the final weights could also become extreme. Note that while random controls used in calibration (as in the case of nr and extreme weights resulting from calibration (for nr and ps adjustments) may have the undesirable effect of inflating the variance, this effect could be offset by the anticipated variance reduction due to the correlation between y and x.