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Estimating Derivatives of Function-Valued Parameters in a Class of Moment Condition Models

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Christoph Rothe, Dominik Wied

Methodology · Submitted 28 Oct 2016

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

The authors' main claim We develop a general approach to estimating the derivative of a function-valued parameter $\theta_o(u)$ that is identified for every value of $u$ as the solution to a moment condition.

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arXiv ID1610.09363 (version 1)
Pith IDPL4LIAZG, Pith's permanent record of this paper and its review
CitationChristoph Rothe, Dominik Wied. "Estimating Derivatives of Function-Valued Parameters in a Class of Moment Condition Models." arXiv:1610.09363 (2016). https://pith.science/paper/PL4LIAZG
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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.06 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.02.

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

We develop a general approach to estimating the derivative of a function-valued parameter $\theta_o(u)$ that is identified for every value of $u$ as the solution to a moment condition. This setup in particular covers many interesting models for conditional distributions, such as quantile regression or distribution regression. Exploiting that $\theta_o(u)$ solves a moment condition, we obtain an explicit expression for its derivative from the Implicit Function Theorem, and estimate the components of this expression by suitable sample analogues, which requires the use of (local linear) smoothing. Our estimator can then be used for a variety of purposes, including the estimation of conditional density functions, quantile partial effects, and structural auction models in economics.

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 We develop a general approach to estimating the derivative of a function-valued parameter $\theta_o(u)$ that is identified for every value of $u$ as the solution to a moment condition. contribution 1.00 0.94 0.31 asserted 1.00
s1 This setup in particular covers many interesting models for conditional distributions, such as quantile regression or distribution regression. background 0.75 0.10 0.04 asserted 0.87
s2 Exploiting that $\theta_o(u)$ solves a moment condition, we obtain an explicit expression for its derivative from the Implicit Function Theorem, and estimate the components of this expression by suitable sample analogues, which requires the use of (local linear) smoothing. method 0.99 0.94 0.23 asserted 1.00
s3 Our estimator can then be used for a variety of purposes, including the estimation of conditional density functions, quantile partial effects, and structural auction models in economics. interpretation 0.59 0.56 0.17 asserted 0.69

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.99.

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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

We develop a general approach to estimating the derivative of a function-valued parameter $\theta_o(u)$ that is identified for every value of $u$ as the solution to a moment condition. This setup in particular covers many interesting models for conditional distributions, such as quantile regression or distribution regression. Exploiting that $\theta_o(u)$ solves a moment condition, we obtain an explicit expression for its derivative from the Implicit Function Theorem, and estimate the components of this expression by suitable sample analogues, which requires the use of (local linear) smoothing. Our estimator can then be used for a variety of purposes, including the estimation of conditional density functions, quantile partial effects, and structural auction models in economics.

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