Uncertainty Quantification for High-Dimensional Sparse Nonparametric Additive Models
TL;DR: In this article, the authors focus on the parametric linear regression problem in high-dimensional settings, which has recently attracted enormous attention within the literature, and most published work focuses on parametric LRL.
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Abstract: Statistical inference in high-dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem....
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Figures
Figure 4: Similar to Figure 5.2 but for the kernel-sieve hybrid estimator. 
Table 2: Empirical coverage rates of confidence intervals for E(Yi|xi). Numbers in parentheses are the average widths of the confidence intervals. 
Figure 5: 95% prediction intervals, denoted as blue error bars, for the responses Yi’s, denoted as black circles. For clarity the Yi’s are sorted in ascending order. 
Figure 2: Empirical coverage rates for each non-zero function with experimental parameters n = 200, p = 1, 000, σ = 0.8, α = 5%, l = 3 and K = 8. 
Table 1: Empirical coverage rates of confidence intervals for σ2. Numbers in parentheses are average widths of the confidence intervals. 
Figure 6: A 95% pointwise confidence band for YXLD at. The black solid line is the median of the fiducial samples and the dashed blue lines represent the confidence band.
Citations
Generalized Fiducial Inference for Threshold Estimation in Dose–Response and Regression Settings
TL;DR: In this paper, the authors apply Fisher's fiducial idea to develop an inference method for these threshold values, which allows the use of multiple parametric relationships to model the underlying pattern of the data and hence, reduces the risk of model mis-specification.
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High-Dimensional Bayesian Inference in Nonparametric Additive Models
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TL;DR: In this article, a fully Bayesian approach is proposed for ultra-high-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small number of components.
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Uncertainty Quantification for Sparse Estimation of Spectral Lines
TL;DR: In this paper , the authors proposed a line spectral estimation method based on the generalized fiducial inference framework, which provides an uncertainty measure for the number of spectral lines and also offers point estimates and confidence intervals for other parameters of interest.
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Uncertainty quantification for honest regression trees
TL;DR: In this paper, a new method is developed for quantifying the uncertainties of the estimates and predictions produced by honest random forests, which is based on the generalized fiducial methodology, and provides a fiducual density function that measures how likely each single honest tree is the true model.
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Uncertainty Quantification in Ensembles of Honest Regression Trees using Generalized Fiducial Inference
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