Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy–Krause variation
通过完全单调性与Hardy–Krause变差推广多元保序回归和总变差去噪
We consider the problem of nonparametric regression when the covariate is d dimensional, where d≥1. In this paper, we introduce and study two nonparametric least squares estimators (LSEs) in this setting—the entirely monotonic LSE and the constrained Hardy–Krause variation LSE. We show that these two LSEs are natural generalizations of univariate isotonic regression and univariate total variation denoising, respectively, to multiple dimensions. We discuss the…