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A model-calibration information-theoretic approach to using complete auxiliary information. (English) Zbl 1125.62003

Summary: We propose a model-calibrated K-L relative entropy minimization (MKLEM) approach to using complete auxiliary information from survey data. Our estimator is asymptotically equivalent to a model-calibration (MC) estimator of C. Wu and R. R. Sitter [J. Am. Stat. Assoc. 96, No. 453, 185–193 (2001; Zbl 1015.62005)] in the case of estimating the finite population mean. One attractive advantage of our MKLEM approach are the intrinsic properties of the resulting weights: \(\hat{p}_i > 0\) and \( \sum_{i \in s}\hat{p}_i=1\) , which make this approach generally applicable to the estimation of distribution functions and quantiles. The resulting estimator \(\hat{F}_{MKL}(y)\) is asymptotically equivalent to a generalized regression estimator and itself a distribution function.

MSC:

62D05 Sampling theory, sample surveys
62G05 Nonparametric estimation

Citations:

Zbl 1015.62005
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