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Estimation and Inference for Upper Hinge Regression Models.

Adam Elder1, Youyi Fong1

  • 1Department of Biostatistics, University of Washington.

Environmental and Ecological Statistics
|June 5, 2023
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Summary
This summary is machine-generated.

We introduce upper hinge models, a novel threshold regression approach. These models efficiently detect associations only below a specific predictor threshold, improving statistical estimation.

Keywords:
Dynamic programmingchange pointecological thresholdsegmented models

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Area of Science:

  • Statistics
  • Ecology

Background:

  • Threshold regression models are crucial for identifying specific predictor-outcome relationships.
  • Existing segmented models can be less efficient due to higher degrees of freedom.

Purpose of the Study:

  • Introduce and evaluate upper hinge models as an efficient alternative.
  • Develop a novel estimation algorithm for these models.

Main Methods:

  • Developed a fast grid search algorithm for estimating upper hinge linear regression models.
  • Derived asymptotic normality for confidence intervals in non-Gaussian upper hinge generalized linear models.

Main Results:

  • The new grid search algorithm significantly reduces computational complexity.
  • Upper hinge models offer greater estimation efficiency compared to segmented models.
  • Proposed methods are validated through numerical experiments and ecological data.

Conclusions:

  • Upper hinge models provide a more efficient approach to threshold regression.
  • The novel algorithm facilitates practical application and robust confidence interval construction.