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Testing model assumptions in functional regression models

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  • Bücher, Axel
  • Dette, Holger
  • Wieczorek, Gabriele

Abstract

In the functional regression model where the responses are curves, new tests for the functional form of the regression and the variance function are proposed, which are based on a stochastic process estimating L2-distances. Our approach avoids the explicit estimation of the functional regression and it is shown that normalized versions of the proposed test statistics converge weakly. The finite sample properties of the tests are illustrated by means of a small simulation study. It is also demonstrated that for small samples, bootstrap versions of the tests improve the quality of the approximation of the nominal level.

Suggested Citation

  • Bücher, Axel & Dette, Holger & Wieczorek, Gabriele, 2011. "Testing model assumptions in functional regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1472-1488, November.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:10:p:1472-1488
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    References listed on IDEAS

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    Cited by:

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    2. Eduardo García‐Portugués & Javier Álvarez‐Liébana & Gonzalo Álvarez‐Pérez & Wenceslao González‐Manteiga, 2021. "A goodness‐of‐fit test for the functional linear model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 502-528, June.
    3. Germán Aneiros & Paula Raña & Philippe Vieu & Juan Vilar, 2018. "Bootstrap in semi-functional partial linear regression under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 659-679, September.

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