Naive Penalized Spline Estimators of Derivatives Achieve Optimal Rates of Convergence
arXiv:2208.10664v11 citationsh-index: 43
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This provides a theoretical guarantee for derivative estimation in regression, which is incremental but useful for statisticians and data analysts.
The paper tackles the problem of estimating derivatives using penalized spline methods, showing that simply differentiating the spline estimator for the mean regression function achieves the optimal L2 convergence rate.
This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding derivative achieves the optimal L2 rate of convergence.