Robust Permutation Tests for Penalized Splines
1
Department of Psychology, University of Minnesota, Minneapolis, MN 55455, USA
2
School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA
Academic Editor: Wei Zhu
Stats 2022, 5(3), 916-933; https://doi.org/10.3390/stats5030053
Received: 18 August 2022
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Revised: 9 September 2022
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Accepted: 11 September 2022
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Published: 16 September 2022
Penalized splines are frequently used in applied research for understanding functional relationships between variables. In most applications, statistical inference for penalized splines is conducted using the random effects or Bayesian interpretation of a smoothing spline. These interpretations can be used to assess the uncertainty of the fitted values and the estimated component functions. However, statistical tests about the nature of the function are more difficult, because such tests often involve testing a null hypothesis that a variance component is equal to zero. Furthermore, valid statistical inference using the random effects or Bayesian interpretation depends on the validity of the utilized parametric assumptions. To overcome these limitations, I propose a flexible and robust permutation testing framework for inference with penalized splines. The proposed approach can be used to test omnibus hypotheses about functional relationships, as well as more flexible hypotheses about conditional relationships. I establish the conditions under which the methods will produce exact results, as well as the asymptotic behavior of the various permutation tests. Additionally, I present extensive simulation results to demonstrate the robustness and superiority of the proposed approach compared to commonly used methods.
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Keywords:
generalized ridge regression; nonparametric methods; penalized least squares; randomization tests; smoothing and nonparametric regression
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
MDPI and ACS Style
Helwig, N.E. Robust Permutation Tests for Penalized Splines. Stats 2022, 5, 916-933. https://doi.org/10.3390/stats5030053
AMA Style
Helwig NE. Robust Permutation Tests for Penalized Splines. Stats. 2022; 5(3):916-933. https://doi.org/10.3390/stats5030053
Chicago/Turabian StyleHelwig, Nathaniel E. 2022. "Robust Permutation Tests for Penalized Splines" Stats 5, no. 3: 916-933. https://doi.org/10.3390/stats5030053
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