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Functional regression with repeated eigenvalues

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  • Reimherr, Matthew

Abstract

We explore the functional principal component method for estimating regression parameters in functional linear models. We demonstrate that the commonly made assumption concerning unique eigenvalues is unnecessary. Convergence rates are established allowing a variety of sample spaces and dependence structures.

Suggested Citation

  • Reimherr, Matthew, 2015. "Functional regression with repeated eigenvalues," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 62-70.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:62-70
    DOI: 10.1016/j.spl.2015.07.037
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    1. Lajos Horváth & Piotr Kokoszka & Ron Reeder, 2013. "Estimation of the mean of functional time series and a two-sample problem," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(1), pages 103-122, January.
    2. Kokoszka, Piotr & Reimherr, Matthew, 2013. "Asymptotic normality of the principal components of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1546-1562.
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    Cited by:

    1. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    2. Petrovich, Justin & Reimherr, Matthew, 2017. "Asymptotic properties of principal component projections with repeated eigenvalues," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 42-48.
    3. Jikai Jin & Yiping Lu & Jose Blanchet & Lexing Ying, 2022. "Minimax Optimal Kernel Operator Learning via Multilevel Training," Papers 2209.14430, arXiv.org, revised Jul 2023.

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