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Rank estimation for the functional linear model

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  • Melody Denhere
  • Huybrechts F. Bindele

Abstract

This article discusses the estimation of the parameter function for a functional linear regression model under heavy-tailed errors' distributions and in the presence of outliers. Standard approaches of reducing the high dimensionality, which is inherent in functional data, are considered. After reducing the functional model to a standard multiple linear regression model, a weighted rank-based procedure is carried out to estimate the regression parameters. A Monte Carlo simulation and a real-world example are used to show the performance of the proposed estimator and a comparison made with the least-squares and least absolute deviation estimators.

Suggested Citation

  • Melody Denhere & Huybrechts F. Bindele, 2016. "Rank estimation for the functional linear model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1928-1944, August.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:10:p:1928-1944
    DOI: 10.1080/02664763.2015.1125863
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    References listed on IDEAS

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    4. Kloke, John D. & McKean, Joseph W. & Rashid, M. Mushfiqur, 2009. "Rank-Based Estimation and Associated Inferences for Linear Models With Cluster Correlated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 384-390.
    5. Gareth M. James, 2002. "Generalized linear models with functional predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 411-432, August.
    6. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
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