Electronic Journal of Statistics

Isotonic regression meets LASSO

Matey Neykov

Full-text: Open access

Abstract

This paper studies a two step procedure for monotone increasing additive single index models with Gaussian designs. The proposed procedure is simple, easy to implement with existing software, and consists of consecutively applying LASSO and isotonic regression. Aside from formalizing this procedure, we provide theoretical guarantees regarding its performance: 1) we show that our procedure controls the in-sample squared error; 2) we demonstrate that one can use the procedure for predicting new observations, by showing that the absolute prediction error can be controlled with high-probability. Our bounds show a tradeoff of two rates: the minimax rate for estimating high dimensional quadratic loss, and the minimax nonparametric rate for estimating a monotone increasing function.

Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 710-746.

Dates
Received: February 2018
First available in Project Euclid: 20 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1550632213

Digital Object Identifier
doi:10.1214/19-EJS1537

Mathematical Reviews number (MathSciNet)
MR3914933

Zentralblatt MATH identifier
07038002

Keywords
Monotone single index models isotonic regression LASSO sparsity high dimensional statistics

Rights
Creative Commons Attribution 4.0 International License.

Citation

Neykov, Matey. Isotonic regression meets LASSO. Electron. J. Statist. 13 (2019), no. 1, 710--746. doi:10.1214/19-EJS1537. https://projecteuclid.org/euclid.ejs/1550632213


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