scholarly journals UNIFORM-IN-SUBMODEL BOUNDS FOR LINEAR REGRESSION IN A MODEL-FREE FRAMEWORK

2021 ◽  
pp. 1-47
Author(s):  
Arun K. Kuchibhotla ◽  
Lawrence D. Brown ◽  
Andreas Buja ◽  
Edward I. George ◽  
Linda Zhao
Keyword(s):  
Model Selection ◽  
Linear Regression ◽  
Estimation Error ◽  
Linear Representation ◽  
High Dimensional ◽  
Model Free ◽  
Classical Technique ◽  
Regression Estimators ◽  
Classical Linear Regression ◽  
Linear Regression Estimator

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional estimation techniques can be seen as variable selection that leads to a smaller set of variables (a “submodel”) where classical linear regression applies. We analyze linear regression estimators resulting from model selection by proving estimation error and linear representation bounds uniformly over sets of submodels. Based on deterministic inequalities, our results provide “good” rates when applied to both independent and dependent data. These results are useful in meaningfully interpreting the linear regression estimator obtained after exploring and reducing the variables and also in justifying post-model-selection inference. All results are derived under no model assumptions and are nonasymptotic in nature.

scholarly journals Variable Selection Using Nonlocal Priors in High-Dimensional Generalized Linear Models With Application to fMRI Data Analysis

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 807
Author(s):  
Xuan Cao ◽  
Kyoungjae Lee
Keyword(s):  
Model Selection ◽  
Linear Regression ◽  
Variable Selection ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Real Data ◽  
High Dimensional ◽  
Model Selection Consistency ◽  
Fmri Study ◽  
Dimensional Variable

High-dimensional variable selection is an important research topic in modern statistics. While methods using nonlocal priors have been thoroughly studied for variable selection in linear regression, the crucial high-dimensional model selection properties for nonlocal priors in generalized linear models have not been investigated. In this paper, we consider a hierarchical generalized linear regression model with the product moment nonlocal prior over coefficients and examine its properties. Under standard regularity assumptions, we establish strong model selection consistency in a high-dimensional setting, where the number of covariates is allowed to increase at a sub-exponential rate with the sample size. The Laplace approximation is implemented for computing the posterior probabilities and the shotgun stochastic search procedure is suggested for exploring the posterior space. The proposed method is validated through simulation studies and illustrated by a real data example on functional activity analysis in fMRI study for predicting Parkinson’s disease.

Optimal model-free fuzzy logic control for autonomous unmanned aerial vehicle

2021 ◽  
pp. 095441002110253
Author(s):  
Hossam E Glida ◽  
Latifa Abdou ◽  
Abdelghani Chelihi ◽  
Chouki Sentouh ◽  
Gabriele Perozzi
Keyword(s):  
Fuzzy Logic ◽  
Unmanned Aerial Vehicle ◽  
Fuzzy Logic Control ◽  
Estimation Error ◽  
Design Parameters ◽  
Multiple Model ◽  
Optimal Model ◽  
Model Free ◽  
Logic Control ◽  
Aerial Vehicle

This article deals with the issue of designing a flight tracking controller for an unmanned aerial vehicle type of quadrotor based on an optimal model-free fuzzy logic control approach. The main design objective is to perform an automatic flight trajectory tracking under multiple model uncertainties related to the knowledge of the nonlinear dynamics of the system. The optimal control is also addressed taking into consideration unknown external disturbances. To achieve this goal, we propose a new optimal model-free fuzzy logic–based decentralized control strategy where the influence of the interconnection term between the subsystems is minimized. A model-free controller is firstly designed to achieve the convergence of the tracking error. For this purpose, an adaptive estimator is proposed to ensure the approximation of the nonlinear dynamic functions of the quadrotor. The fuzzy logic compensator is then introduced to deal with the estimation error. Moreover, the optimization problem to select the optimal design parameters of the proposed controller is solved using the bat algorithm. Finally, a numerical validation based on the Parrot drone platform is conducted to demonstrate the effectiveness of the proposed control method with various flying scenarios.

scholarly journals SPReM: Sparse Projection Regression Model For High-Dimensional Linear Regression

2015 ◽  
Vol 110 (509) ◽  
pp. 289-302 ◽  
Author(s):  
Qiang Sun ◽  
Hongtu Zhu ◽  
Yufeng Liu ◽  
Joseph G. Ibrahim
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
High Dimensional ◽  
Sparse Projection

Functional Linear Regression

2018 ◽  
Author(s):  
Hervé Cardot ◽  
Pascal Sarda
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Estimation Error ◽  
Asymptotic Properties ◽  
Principal Component Regression ◽  
Principal Component ◽  
Penalized Least Squares ◽  
Open Problems ◽  
Functional Linear Regression

This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.

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