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Asymptotic Theory of $L$-Statistics and Integrable Empirical Processes

Tetsuya Kaji

arXiv 16 Oct 2019 · Mathematics — Statistics Theory · 2 citations (OpenAlex)

arXiv:1910.07572 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to asymptotically linear estimators. The key idea is to consider empirical processes in the spaces appropriate for integration. First, we characterize weak convergence of empirical distribution functions and random weight functions in the space of bounded integrable functions. Second, we establish the delta method for empirical quantile functions as integrable functions. Third, we derive the delta method for $L$-statistics. Finally, we prove weak convergence of their bootstrap processes, showing validity of nonparametric bootstrap.

Citation extraction

17
references
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in-text mentions
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distinct cited
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main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1bbook[author] van der Vaart, Aad W.A. W. Wellner, Jon A.J. A (1996) )0.97629593%
2bbook[author] Csörg o, MiklósM. Horváth, LajosL (1993) )0.64422100%
3bbook[author] Shorack, Galen R.G. R. Wellner, Jon A.J. A (1986) )0.64422100%
4barticle[author] Acemoglu, DaronD., Naidu, SureshS., Restrepo, Pascu… (2019) )0.58510230%
5barticle[author] Acemoglu, DaronD., Johnson, SimonS., Kermani, AmirA… (2016) )0.51121100%
6barticle[author] Acemoglu, DaronD., Johnson, SimonS. Robinson, James… (2001) )0.51121100%
7barticle[author] Shorack, Galen R.G. R (1997) )0.51121100%
8barticle[author] Agarwal, NikhilN., Banternghansa, ChanontC. Bui, Li… (2010) )0.40511100%
9bunpublished[author] Banerjee, AbhijitA., Duflo, EstherE. Hornbeck,… (2014) )0.40511100%
10barticle[author] del Barrio, EustasioE., Giné, EvaristE. Matrán, Car… (1999) )0.40511100%

Showing the top 10 of 17 scored citations.

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