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Stable Asymptotics for M-estimators

Published in International Statistical Review. 2015, no. april, p. 1-24
Abstract We review some first-and higher-order asymptotic techniques for M-estimators and we study their stability in the presence of data contaminations. We show that the estimating function (ψ) and its derivative with respect to the parameter (∇ θ ⊤ ψ) play a central role. We discuss in detail the first-order Gaussian density approximation, saddlepoint density approximation, saddlepoint test, tail area approximation via Lugannani-Rice formula, and empirical saddlepoint density approximation (a technique related to the empirical likelihood method). For all these asymptotics, we show that a bounded (in the Euclidean norm) ψ and a bounded (e.g., in the Frobenius norm) ∇ θ ⊤ ψ yield stable inference in the presence of data contamination. We motivate and illustrate our findings by theoretical and numerical examples about the benchmark case of one-dimensional location model.
Keywords Edgeworth expansionEmpirical likelihoodHigher-orderInfinitesimal robustnessP-valueRedescending M-estimatorRelative errorSaddlepoint techniquesVon Mises expansion
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LA VECCHIA, Davide. Stable Asymptotics for M-estimators. In: International Statistical Review, 2015, n° april, p. 1-24. doi: 10.1111/insr.12102 https://archive-ouverte.unige.ch/unige:75148

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Deposited on : 2015-09-13

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