Curve fitting and jump detection on nonparametric regression with missing data.

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Nonparametric regression models are widely used for data analysis.
• Missing data in the response variable presents a significant challenge in regression analysis.
• Accurate estimation of regression functions, especially those with discontinuities (jumps), is crucial.

Purpose of the Study:

• To develop a novel jump-preserving estimation method for nonparametric regression models with missing response data.
• To address the challenges posed by missing data in estimating regression functions.
• To ensure the accurate identification and preservation of jumps in the underlying regression function.

Main Methods:

• Utilized the inverse probability weighted technique to handle missing response data.
• Employed local piecewise-linear expansion with left and right kernels to approximate the unknown regression function.
• Developed left- and right-limit estimators at observed points and determined final estimators via residual sums of squares.

Main Results:

• Established the convergence rate for the proposed estimators.
• Demonstrated the effectiveness of the method through simulation studies.
• Validated the approach using a real-world example of conjunctivitis data.

Conclusions:

• The proposed inverse probability weighted, jump-preserving estimation method is effective for nonparametric regression with missing response data.
• The method accurately estimates regression functions while preserving important discontinuities.
• The approach shows promise for applications in various fields requiring robust regression analysis.