Estimation and Inference for Upper Hinge Regression Models

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.