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Testing Linear Operator Constraints in Functional Response Regression with Incomplete Response Functions.

Yeonjoo Park1, Kyunghee Han2, Douglas G Simpson3

  • 1Department of Management Science and Statistics, University of Texas at San Antonio, San Antonio, TX.

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Summary
This summary is machine-generated.

This study introduces hypothesis testing for function-on-scalar regression with incomplete data. The methods handle various data gaps, enabling robust statistical inferences on functional coefficients.

Keywords:
Function-on-scalar regressionPrimary 62R10incomplete observationsmeasurement errorspartially observed functional datasecondary 62G20shape constraints hypothesis

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Function-on-scalar regression is vital for analyzing data where predictors are functions and outcomes are scalars.
  • Incomplete functional responses pose challenges for traditional statistical inference.

Purpose of the Study:

  • To develop hypothesis testing procedures for linear operator constraints in function-on-scalar regression with incomplete functional responses.
  • To provide a unified framework for statistical inferences on functional regression coefficients across three sampling scenarios.

Main Methods:

  • Developing hypothesis testing procedures to assess linear operator constraints.
  • Utilizing integrated -distance to measure deviations from constraint spaces.
  • Establishing large sample properties: consistency, asymptotic distribution, and local power.

Main Results:

  • The proposed test procedure demonstrates consistency, asymptotic distribution, and local power.
  • A simulation study confirms the finite sample power and level of the test across various scenarios.
  • The methodology is validated through applications to U.S. obesity prevalence and automotive ergonomics motion analysis.

Conclusions:

  • The developed methods offer a robust framework for hypothesis testing in function-on-scalar regression with incomplete data.
  • The approach is applicable to diverse real-world datasets, including those with complex missing data structures.