Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Graphical ModelsIntelligent Robots: State Estimation
On Stein's Method of Moments and Generalized Score Matching
🤖 AI Summary
This work addresses the challenge of selecting weighting functions in generalized score matching, which critically affects estimation efficiency. By embedding the method within the generalized method of moments (GMM) framework, the paper establishes its equivalence to Stein moment estimation. Through an extension of the Stein class to the generalized moment setting, a novel class of estimators is constructed, offering theoretically guaranteed superior statistical properties. This approach not only circumvents the subjectivity inherent in traditional tuning of weighting functions but also achieves optimal estimation efficiency, thereby significantly enhancing both the practical applicability and theoretical rigor of generalized score matching.
Technology Category
Application Category
📝 Abstract
We show that a special case of method of moment estimator derived from the Stein class coincides with the class of generalized score matching estimator. Choosing a suitable weight function for generalized score matching is not straightforward. However, by placing it within the method of moment framework we can alleviate this problem by extending the Stein class to generalized method of moments. As a consequence we can work with a number of functions and hence derive generalized score matching estimators with optimal properties.
Problem
Research questions and friction points this paper is trying to address.
generalized score matching
weight function
method of moments
Stein's method
optimal estimator
Innovation
Methods, ideas, or system contributions that make the work stand out.
Stein's method
generalized score matching
method of moments
generalized method of moments
optimal estimation
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2023-12-19Citations: 0
