Errors-in-variables jump regression using local clustering.

Area of Science:

• Econometrics
• Statistical Modeling
• Data Analysis

Background:

• Errors-in-variables (EIV) regression is common in econometrics.
• Analyzing discontinuous regression functions with unknown measurement error distributions is challenging.
• Existing jump regression methods often require no measurement error or pre-detected jumps.

Purpose of the Study:

• To develop a novel method for reconstructing jump regression curves from data with measurement error.
• To address the limitations of existing methods that struggle with unknown error distributions and masked jump structures.
• To estimate regression functions while preserving inherent jumps.

Main Methods:

• Proposed a direct jump-preserving method for EIV regression.
• Utilized local clustering to handle measurement error masking jump structures.
• No explicit jump detection is required prior to estimation.

Main Results:

• The proposed curve estimator is statistically consistent.
• The method effectively preserves jump structures masked by measurement error.
• Numerical comparisons demonstrate superior jump-preserving properties.

Conclusions:

• The developed method offers a robust solution for jump regression with measurement error.
• It provides a valuable tool for analyzing complex data where jumps are critical.
• The approach was successfully applied to a health tax policy study in Australia.