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Estimation and inference for multikink expectile regression with longitudinal data.

Dongyu Li1, Lei Wang1, Weihua Zhao2

  • 1School of Statistics and Data Science & LPMC, Nankai University, Tianjin, China.

Statistics in Medicine
|December 9, 2021
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Summary
This summary is machine-generated.

This study introduces a new longitudinal multikink expectile regression model for analyzing complex data. The proposed methods accurately estimate kink points and provide reliable statistical inference, showing good performance in simulations.

Keywords:
bootstraphypothesis testingkink pointslongitudinal expectile regressionmodel selection

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Area of Science:

  • Statistics
  • Econometrics
  • Longitudinal Data Analysis

Background:

  • Longitudinal data analysis requires robust models for complex patterns.
  • Existing regression models may not adequately capture abrupt changes (kinks) in longitudinal data.
  • Expectile regression offers an alternative to quantile regression for analyzing conditional properties.

Purpose of the Study:

  • To develop a longitudinal multikink expectile regression model.
  • To propose methods for parameter estimation, kink point detection, and statistical inference.
  • To assess the performance of the new model and methods through simulations and real-world data.

Main Methods:

  • A bootstrap restarting iterative algorithm for parameter and kink location estimation.
  • A modified Bayesian Information Criterion (BIC) for estimating the number of kink points.
  • A weighted cumulative sum (WCUSUM) statistic for testing kink effects.

Main Results:

  • The proposed estimators achieve root-n consistency for kink locations.
  • Theoretical consistency and asymptotic normality are demonstrated for all estimators.
  • Simulation studies confirm desirable finite sample performance under various error conditions.
  • The WCUSUM test effectively detects kink effects at specified expectiles.

Conclusions:

  • The developed longitudinal multikink expectile regression model provides a powerful tool for analyzing complex longitudinal data.
  • The proposed estimation and testing procedures are statistically sound and perform well in practice.
  • The methods are applicable to diverse fields, as demonstrated by real data applications.