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A hat matrix for monotonicity constrained B-spline and P-spline regression

Author

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  • Kagerer, Kathrin

Abstract

Splines constitute an interesting way to flexibly estimate a nonlinear relationship between several covariates and a response variable using linear regression techniques. The popularity of splines is due to their easy application and hence the low computational costs since their basis functions can be added to the regression model like usual covariates. As long as no inequality constraints and penalties are imposed on the estimation, the degrees of freedom of the model estimation can be determined straightforwardly as the number of estimated parameters. This paper derives a formula for computing the hat matrix of a penalized and inequality constrained splines estimator. Its trace gives the degrees of freedom of the model estimation which are necessary for the calculation of several information criteria that can be used e.g. for specifying the parameters for the spline or for model selection.

Suggested Citation

  • Kagerer, Kathrin, 2015. "A hat matrix for monotonicity constrained B-spline and P-spline regression," University of Regensburg Working Papers in Business, Economics and Management Information Systems 484, University of Regensburg, Department of Economics.
    • Handle: RePEc:bay:rdwiwi:31450
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    File URL: https://epub.uni-regensburg.de/31450/1/DP484_Kagerer_hat_matrix_constr_splines.pdf
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    References listed on IDEAS

    as
    1. Paula, Gilberto A., 1993. "Assessing local influence in restricted regression models," Computational Statistics & Data Analysis, Elsevier, vol. 16(1), pages 63-79, June.
    2. Kagerer, Kathrin, 2013. "A short introduction to splines in least squares regression analysis," University of Regensburg Working Papers in Business, Economics and Management Information Systems 472, University of Regensburg, Department of Economics.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Spline; monotonicity; penalty; hat matrix; regression; Monte Carlo simulation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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