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Establishing a Competing Risk Regression Nomogram Model for Survival Data

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Published on: October 23, 2020

Testing conditional quantile independence with functional covariate.

Yongzhen Feng¹, Jie Li², Xiaojun Song³

¹Center for Statistical Science and Department of Industrial Engineering, Tsinghua University, Beijing 100084, China.

|May 14, 2024

Summary

This summary is machine-generated.

This study introduces a novel non-parametric conditional independence test for functional data, effectively addressing the curse of dimensionality. The proposed method demonstrates strong power in detecting dependencies, validated by simulations and EEG data analysis.

Keywords:

empirical process functional data multiplier bootstrap quantile independence random projections

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Area of Science:

Statistics
Functional Data Analysis
Non-parametric Statistics

Background:

Conditional independence testing is crucial in statistical modeling.
Existing methods often struggle with high-dimensional functional covariates.
The curse of dimensionality poses a significant challenge in functional data analysis.

Purpose of the Study:

To develop a new non-parametric conditional independence test for scalar response and functional covariate.
To address the curse of dimensionality in functional data analysis.
To provide a versatile statistical tool for analyzing complex datasets.

Main Methods:

A Cramer-von Mises type test statistic is constructed using an empirical process.
Random projections of the functional covariate are employed to mitigate dimensionality.
Asymptotic null distribution and power properties are derived under mild assumptions.
Multiplier bootstrap is proposed for critical value estimation.

Main Results:

The proposed test effectively avoids the curse of dimensionality under the null hypothesis.
The test statistic exhibits desirable asymptotic global and local power properties.
It can detect local alternatives converging at a parametric rate.
Monte Carlo simulations confirm good finite-sample performance.

Conclusions:

The developed non-parametric test offers a powerful and computationally efficient solution for conditional independence testing with functional covariates.
The method's utility is demonstrated through practical application to EEG data.
This approach enhances statistical inference in fields utilizing functional data.