{"ID":2855392,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.14055","arxiv_id":"2510.14055","title":"Minimum Hellinger Distance Estimators for Complex Survey Designs","abstract":"Reliable inference from complex survey samples can be derailed by outliers and high-leverage observations induced by unequal inclusion probabilities and calibration. We develop a minimum Hellinger distance estimator (MHDE) for parametric superpopulation models under complex designs, including Poisson PPS and fixed-size SRS/PPS without replacement, with possibly stochastic post-stratified or calibrated weights. Using a Horvitz-Thompson-adjusted kernel density plug-in, we show: (i) $L^1$-consistency of the KDE with explicit large-deviation tail bounds driven by a variance-adaptive effective sample size; (ii) uniform exponential bounds for the Hellinger affinity that yield MHDE consistency under mild identifiability; (iii) an asymptotic Normal distribution for the MHDE with covariance $\\mathbf A^{-1}\\boldsymbolΣ\\mathbf A^{\\intercal}$ (and a finite-population correction under without-replacement designs); and (iv) robustness via the influence function and $α$-influence curves in the Hellinger topology. Simulations under Gamma and lognormal superpopulation models quantify efficiency-robustness trade-offs relative to weighted MLE under independent and high-leverage contamination. An application to NHANES 2021-2023 total water consumption shows that the MHDE remains stable despite extreme responses that markedly bias the MLE. The estimator is simple to implement via quadrature over a fixed grid and is extensible to other divergence families.","short_abstract":"Reliable inference from complex survey samples can be derailed by outliers and high-leverage observations induced by unequal inclusion probabilities and calibration. We develop a minimum Hellinger distance estimator (MHDE) for parametric superpopulation models under complex designs, including Poisson PPS and fixed-size...","url_abs":"https://arxiv.org/abs/2510.14055","url_pdf":"https://arxiv.org/pdf/2510.14055v2","authors":"[\"David Kepplinger\",\"Anand N. Vidyashankar\"]","published":"2025-10-15T19:47:56Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"cs.IT\",\"math.PR\"]","methods":"[]","has_code":false}