Corpus ID: 216080858

On a phase transition in general order spline regression

@article{Shen2020OnAP,
  title={On a phase transition in general order spline regression},
  author={Yandi Shen and Qiyang Han and Fang Han},
  journal={arXiv: Statistics Theory},
  year={2020}
}
In the Gaussian sequence model $Y= \theta_0 + \varepsilon$ in $\mathbb{R}^n$, we study the fundamental limit of approximating the signal $\theta_0$ by a class $\Theta(d,d_0,k)$ of (generalized) splines with free knots. Here $d$ is the degree of the spline, $d_0$ is the order of differentiability at each inner knot, and $k$ is the maximal number of pieces. We show that, given any integer $d\geq 0$ and $d_0\in\{-1,0,\ldots,d-1\}$, the minimax rate of estimation over $\Theta(d,d_0,k)$ exhibits the… Expand

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