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On the validity of the bootstrap hypothesis testing in functional linear regression

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  • Omid Khademnoe

    (University of Zanjan)

  • S. Mohammad E. Hosseini-Nasab

    (Shahid Beheshti University)

Abstract

We consider a functional linear regression model with functional predictor and scalar response. For this model, a procedure to test the slope function based on projecting the slope function onto an arbitrary $$ L^2 $$ L 2 basis has been introduced in the literature. We propose its bootstrap counterpart for testing the slope function, and obtain the asymptotic null distributions of the tests statistics and the asymptotic powers of the tests. Finally, we conduct a simulation study to evaluate the accuracy of the two tests procedures. As a practical illustration, we use the Export Development Bank of Iran dataset, and test the nullity of the slope function of a model predicting total annual noncurrent balance of facilities based on current balance of facilities.

Suggested Citation

  • Omid Khademnoe & S. Mohammad E. Hosseini-Nasab, 2024. "On the validity of the bootstrap hypothesis testing in functional linear regression," Statistical Papers, Springer, vol. 65(4), pages 2361-2396, June.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:4:d:10.1007_s00362-023-01488-z
    DOI: 10.1007/s00362-023-01488-z
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    References listed on IDEAS

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    1. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    2. Hervé Cardot & Frédéric Ferraty & André Mas & Pascal Sarda, 2003. "Testing Hypotheses in the Functional Linear Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 241-255, March.
    3. Peter Hall & You‐Jun Yang, 2010. "Ordering and selecting components in multivariate or functional data linear prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 93-110, January.
    4. Yu-Ru Su & Chong-Zhi Di & Li Hsu, 2017. "Hypothesis testing in functional linear models," Biometrics, The International Biometric Society, vol. 73(2), pages 551-561, June.
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