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Statistical inference for discretely sampled stochastic functional differential equations with small noise

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Hiroki Nemoto, Yasutaka Shimizu

Statistics Theory · Submitted 20 Mar 2023

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

The authors' main claim We show consistency and asymptotic normality of the minimum-contrast estimator when the dispersion coefficient goes to zero and the sample size goes to infinity, simultaneously.

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arXiv ID2303.10807 (version 1)
Pith IDMSJMQHXK, Pith's permanent record of this paper and its review
CitationHiroki Nemoto, Yasutaka Shimizu. "Statistical inference for discretely sampled stochastic functional differential equations with small noise." arXiv:2303.10807 (2023). https://pith.science/paper/MSJMQHXK
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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, 3,514 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast function is based on a local-Gauss approximation to the transition probability density of the process. We show consistency and asymptotic normality of the minimum-contrast estimator when the dispersion coefficient goes to zero and the sample size goes to infinity, simultaneously.

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 Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. background 0.58 0.57 0.06 asserted 0.88
s1 The delay structure is written as an integral form with respect to a delay measure. method 0.96 0.70 0.02 asserted 1.00
s2 Our contrast function is based on a local-Gauss approximation to the transition probability density of the process. method 0.99 0.86 0.04 asserted 1.00
s3 We show consistency and asymptotic normality of the minimum-contrast estimator when the dispersion coefficient goes to zero and the sample size goes to infinity, simultaneously. result 0.98 0.96 0.85 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.68 · evidence from proof or derivation 1.00.

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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

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast function is based on a local-Gauss approximation to the transition probability density of the process. We show consistency and asymptotic normality of the minimum-contrast estimator when the dispersion coefficient goes to zero and the sample size goes to infinity, simultaneously.

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