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The hat matrix for smoothing splines

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  • Eubank, R. L.

Abstract

The matrix which transforms the data vector to the vector of fitted values for smoothing splines is termed the hat matrix. This matrix is shown to have many of the same properties, and is seen to play the same role in the variances and covariances of the residuals, as its regression analysis counterpart. This fact is utilized to propose several possible diagnostic measures for use with smoothing splines. The extension of these results to include multivariate Laplacian smoothing spline is also indicated.

Suggested Citation

  • Eubank, R. L., 1984. "The hat matrix for smoothing splines," Statistics & Probability Letters, Elsevier, vol. 2(1), pages 9-14, January.
    • Handle: RePEc:eee:stapro:v:2:y:1984:i:1:p:9-14
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    Cited by:

    1. Germán Ibacache-Pulgar & Gilberto Paula & Francisco Cysneiros, 2013. "Semiparametric additive models under symmetric distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 103-121, March.
    2. Manghi, Roberto F. & Cysneiros, Francisco José A. & Paula, Gilberto A., 2019. "Generalized additive partial linear models for analyzing correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 47-60.
    3. Germán Ibacache-Pulgar & Cristian Villegas & Javier Linkolk López-Gonzales & Magaly Moraga, 2023. "Influence measures in nonparametric regression model with symmetric random errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 1-25, March.
    4. Schimek, Michael G. & Turlach, Berwin A., 1998. "Additive and generalized additive models: A survey," SFB 373 Discussion Papers 1998,97, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.

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