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Testing model assumptions in functional regression models

Author

Listed:
  • 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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    1. Philippe Besse & J. Ramsay, 1986. "Principal components analysis of sampled functions," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 285-311, June.
    2. André Mas, 2007. "Testing for the Mean of Random Curves: A Penalization Approach," Statistical Inference for Stochastic Processes, Springer, vol. 10(2), pages 147-163, July.
    3. Stefanie Biedermann & Holger Dette, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 417-438, December.
    4. Hervé Cardot, 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.
    5. Biedermann, Stefanie & Dette, Holger, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," Technical Reports 2000,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    7. Hlubinka, Daniel & Prchal, Lubos, 2007. "Changes in atmospheric radiation from the statistical point of view," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4926-4941, June.
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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.

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