Effects of design and error on normal convergence rates in regression problems

1990 ◽  
Vol 85 (3) ◽  
pp. 283-305
Author(s):  
Peter Hall
Keyword(s):  
Convergence Rates ◽  
Normal Convergence ◽  
Regression Problems

scholarly journals New Insights Into Learning With Correntropy-Based Regression

2021 ◽  
Vol 33 (1) ◽  
pp. 157-173
Author(s):  
Yunlong Feng
Keyword(s):  
Minimum Distance ◽  
Convergence Rates ◽  
Distance Estimation ◽  
Information Theoretic Learning ◽  
Conditional Mean ◽  
Conditional Median ◽  
Conditional Mode ◽  
Big Picture ◽  
Regression Problems ◽  
Mean Function

Stemming from information-theoretic learning, the correntropy criterion and its applications to machine learning tasks have been extensively studied and explored. Its application to regression problems leads to the robustness-enhanced regression paradigm: correntropy-based regression. Having drawn a great variety of successful real-world applications, its theoretical properties have also been investigated recently in a series of studies from a statistical learning viewpoint. The resulting big picture is that correntropy-based regression regresses toward the conditional mode function or the conditional mean function robustly under certain conditions. Continuing this trend and going further, in this study, we report some new insights into this problem. First, we show that under the additive noise regression model, such a regression paradigm can be deduced from minimum distance estimation, implying that the resulting estimator is essentially a minimum distance estimator and thus possesses robustness properties. Second, we show that the regression paradigm in fact provides a unified approach to regression problems in that it approaches the conditional mean, the conditional mode, and the conditional median functions under certain conditions. Third, we present some new results when it is used to learn the conditional mean function by developing its error bounds and exponential convergence rates under conditional ([Formula: see text])-moment assumptions. The saturation effect on the established convergence rates, which was observed under ([Formula: see text])-moment assumptions, still occurs, indicating the inherent bias of the regression estimator. These novel insights deepen our understanding of correntropy-based regression, help cement the theoretic correntropy framework, and enable us to investigate learning schemes induced by general bounded nonconvex loss functions.

scholarly journals Analysis of Testing‐Based Forward Model Selection

Econometrica ◽  
2020 ◽  
Vol 88 (5) ◽  
pp. 2147-2173 ◽  
Author(s):  
Damian Kozbur
Keyword(s):  
Model Selection ◽  
Predictive Power ◽  
Convergence Rates ◽  
Forward Model ◽  
Statistical Hypothesis ◽  
Standard Errors ◽  
Regularity Conditions ◽  
Regression Problems ◽  
Heteroscedastic Data

This paper analyzes a procedure called Testing‐Based Forward Model Selection (TBFMS) in linear regression problems. This procedure inductively selects covariates that add predictive power into a working statistical model before estimating a final regression. The criterion for deciding which covariate to include next and when to stop including covariates is derived from a profile of traditional statistical hypothesis tests. This paper proves probabilistic bounds, which depend on the quality of the tests, for prediction error and the number of selected covariates. As an example, the bounds are then specialized to a case with heteroscedastic data, with tests constructed with the help of Huber–Eicker–White standard errors. Under the assumed regularity conditions, these tests lead to estimation convergence rates matching other common high‐dimensional estimators including Lasso.

Convergence Rates for Penalized Least Squares Estimators in PDE Constrained Regression Problems

2020 ◽  
Vol 8 (1) ◽  
pp. 374-413 ◽  
Author(s):  
Richard Nickl ◽  
Sara van de Geer ◽  
Sven Wang
Keyword(s):  
Least Squares ◽  
Convergence Rates ◽  
Penalized Least Squares ◽  
Constrained Regression ◽  
Least Squares Estimators ◽  
Regression Problems

THE CONVERGENCE RATES OF ASYMPTOTICALLY BAYES DISCRIMINATION

1985 ◽  
Vol 5 (1) ◽  
pp. 67-78
Author(s):  
Laisheng Wei
Keyword(s):  
Convergence Rates

Iteration matrices and convergence rates of projection methods

1975 ◽  
Author(s):  
Anthony Seaton Ridolfo
Keyword(s):  
Convergence Rates ◽  
Projection Methods

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

Convergence Rates for Diffusions on Continuous-Time Lattices

2007 ◽  
Author(s):  
Claudio Albanese ◽  
Aleksandar Mijatovic
Keyword(s):  
Continuous Time ◽  
Convergence Rates

scholarly journals Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

2021 ◽  
Author(s):  
Radu Boţ ◽  
Guozhi Dong ◽  
Peter Elbau ◽  
Otmar Scherzer
Keyword(s):  
Linear Operator ◽  
Operator Equation ◽  
Convex Analysis ◽  
Convergence Rates ◽  
Linear Operator Equation ◽  
Optimal Convergence Rates ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Given ◽  
Theoretical Results

AbstractRecently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

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