Minimax-rate adaptive nonparametric regression with unknown correlations of errors

2019 ◽  
Vol 62 (2) ◽  
pp. 227-244
Author(s):  
Guowu Yang ◽  
Yuhong Yang
Keyword(s):  
Nonparametric Regression ◽  
Rate Adaptive ◽  
Minimax Rate

scholarly journals Nonparametric regression with adaptive truncation via a convex hierarchical penalty

Biometrika ◽  
2018 ◽  
Vol 106 (1) ◽  
pp. 87-107
Author(s):  
Asad Haris ◽  
Ali Shojaie ◽  
Noah Simon
Keyword(s):  
Nonparametric Regression ◽  
Empirical Studies ◽  
Finite Basis ◽  
Additive Models ◽  
Computationally Efficient ◽  
Penalized Estimation ◽  
Minimax Rates ◽  
Minimax Rate ◽  
Finite Basis Representation ◽  
Different Levels

SUMMARY We consider the problem of nonparametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well suited to high-dimensional sparse additive models and combines the appealing features of finite basis representation and smoothing penalties. In the case of additive models, a finite basis representation provides a parsimonious representation for fitted functions but is not adaptive when component functions possess different levels of complexity. In contrast, a smoothing spline-type penalty on the component functions is adaptive but does not provide a parsimonious representation. Our proposal simultaneously achieves parsimony and adaptivity in a computationally efficient way. We demonstrate these properties through empirical studies and show that our estimator converges at the minimax rate for functions within a hierarchical class. We further establish minimax rates for a large class of sparse additive models. We also develop an efficient algorithm that scales similarly to the lasso with the number of covariates and sample size.

scholarly journals Mixture Model Nonparametric Regression and Its Application

2021 ◽  
Vol 1842 (1) ◽  
pp. 012044
Author(s):  
Narita Yuri Adrianingsih ◽  
I Nyoman Budiantara ◽  
Jerry Dwi Trijoyo Purnomo
Keyword(s):  
Nonparametric Regression ◽  
Mixture Model
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