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Approximations for the boundary crossing probabilities of moving sums of normal random variables

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Jack Noonan, Anatoly Zhigljavsky

Statistics Theory · Submitted 22 Oct 2018

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

The authors' main claim These results show that the developed approximation is very accurate even for small window length.

how it is stated · asserted 1.00 read the record →

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arXiv ID1810.09229 (version 2)
Pith IDXLKUM4VH, Pith's permanent record of this paper and its review
CitationAnatoly Zhigljavsky, Jack Noonan. "Approximations for the boundary crossing probabilities of moving sums of normal random variables." arXiv:1810.09229 (2018). https://pith.science/paper/XLKUM4VH
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The compiled record

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, 4,171 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.89 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this paper we study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem with a continuous time problem allowing us to apply developed theory for stationary Gaussian processes and to consider a number of approximations (some well known and some not). We bring particular attention to the strong performance of a newly developed approximation that corrects the use of continuous time results in a discrete time setting. Results of extensive numerical comparisons are reported. These results show that the developed approximation is very accurate even for small window length.

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 study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. background 0.52 0.73 0.04 asserted 0.74
s1 We propose approximating a discrete time problem with a continuous time problem allowing us to apply developed theory for stationary Gaussian processes and to consider a number of approximations (some well known and some not). method 0.93 0.90 0.06 asserted 0.97
s2 We bring particular attention to the strong performance of a newly developed approximation that corrects the use of continuous time results in a discrete time setting. contribution 0.63 0.78 0.57 asserted 0.97
s3 Results of extensive numerical comparisons are reported. contribution 0.45 0.89 0.03 asserted 0.79
s4 These results show that the developed approximation is very accurate even for small window length. result 0.86 0.94 0.67 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.94 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem with a continuous time problem allowing us to apply developed theory for stationary Gaussian processes and to consider a number of approximations (some well known and some not). We bring particular attention to the strong performance of a newly developed approximation that corrects the use of continuous time results in a discrete time setting. Results of extensive numerical comparisons are reported. These results show that the developed approximation is very accurate even for small window length.

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1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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