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Modification of Moment-Based Tail Index Estimator: Sums versus Maxima

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Natalia Markovich, Marijus Vaičiulis

Statistics Theory · Submitted 9 Oct 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We establish the consistency and asymptotic normality of the newly proposed estimator for i.i.d. data.

how it is stated · asserted 1.00 read the record →

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arXiv ID1710.03084 (version 1)
Pith ID2YVP77O6, Pith's permanent record of this paper and its review
CitationMarijus Vai\v{c}iulis, Natalia Markovich. "Modification of Moment-Based Tail Index Estimator: Sums versus Maxima." arXiv:1710.03084 (2017). https://pith.science/paper/2YVP77O6
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,161 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.16 · human participants 0.02 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we continue the investigation of the SRCEN estimator of the extreme value index $\gamma$ (or the tail index $\alpha=1/\gamma$) proposed in \cite{MCE} for $\gamma>1/2$. We propose a new estimator based on the local maximum. This, in fact, is a modification of the SRCEN estimator to the case $\gamma>0$. We establish the consistency and asymptotic normality of the newly proposed estimator for i.i.d. data. Also, a short discussion on the comparison of the estimators is included.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we continue the investigation of the SRCEN estimator of the extreme value index $\gamma$ (or the tail index $\alpha=1/\gamma$) proposed in \cite{MCE} for $\gamma>1/2$. background 0.99 0.20 0.04 asserted 0.81
s1 We propose a new estimator based on the local maximum. contribution 0.97 0.92 0.16 asserted 0.99
s2 This, in fact, is a modification of the SRCEN estimator to the case $\gamma>0$. contribution 0.73 0.69 0.13 asserted 1.00
s3 We establish the consistency and asymptotic normality of the newly proposed estimator for i.i.d. data. result 0.90 0.95 0.44 asserted 1.00
s4 Also, a short discussion on the comparison of the estimators is included. contribution 0.91 0.72 0.04 asserted 0.67

What kind of paper the classifier reports this is: method or tool 0.95 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we continue the investigation of the SRCEN estimator of the extreme value index $\gamma$ (or the tail index $\alpha=1/\gamma$) proposed in \cite{MCE} for $\gamma>1/2$. We propose a new estimator based on the local maximum. This, in fact, is a modification of the SRCEN estimator to the case $\gamma>0$. We establish the consistency and asymptotic normality of the newly proposed estimator for i.i.d. data. Also, a short discussion on the comparison of the estimators is included.

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