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• W2014686296 abstract "Abstract Suppose the score function J and its approximation Jn satisfy very mild conditions, and let dK = J dF−1 define K. Then a necessary and sufficient condition for asymptotic normality of the normalized trimmed L-statistic Tn, which places no other restriction on the numbers kn and k′n of trimmed observations, is given. In the untrimmed case the condition reduces to K having finite variance or K being in D(Normal), depending on whether one uses √n norming or general norming. Any distribution in the domain of attraction of any stable is brought into the domain of attraction of the normal by trimming slowly growing numbers kn and k′n. Consistent variance estimation is established in the same generality. Random trimming is also allowed. Uniformity in F and kn and k′n is developed for K beneath an envelope K0, both for normality and consistency of the variance estimate. Bootstrapped versions of these theorems are developed, including a CLT for data analysts with conditions formulated solely in terms of the data. Also, the WLLN holds uniformly in K and (kn, k′n) if and only if the envelope K0 satisfies the known necessary and sufficient condition for X n under a fixed qf K0. A strong law of large numbers for the variance estimator is required, as it is intimately tied to bootstrapping. A short extra step would give the bounded LIL (that is, a.s. consistency of the estimator at the best possible rate). The strong law for variances and this LIL could be treated in the same generality as above, and uniform versions developed. However, all this is only in the technical report version of this paper. The power of the related family of inequalities for qfs on which these proofs rest is fully displayed herein, though the inequalities themselves are in a separate paper." @default.
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• W2014686296 date "1997-04-01" @default.
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• W2014686296 title "Uniform CLT, WLLN, LIL and bootstrapping in a data analytic approach to trimmed L-statistics" @default.
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• W2014686296 doi "https://doi.org/10.1016/s0378-3758(97)00121-3" @default.
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