Variable selection in spatial regression via penalized least squares

2009 ◽  
Vol 37 (4) ◽  
pp. 607-624 ◽  
Author(s):  
Haonan Wang ◽  
Jun Zhu
Keyword(s):  
Variable Selection ◽  
Least Squares ◽  
Spatial Regression ◽  
Penalized Least Squares

scholarly journals Variable Selection and Parameter Estimation with the Atan Regularization Method

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Yanxin Wang ◽  
Li Zhu
Keyword(s):  
Parameter Estimation ◽  
Variable Selection ◽  
Least Squares ◽  
Regularization Method ◽  
High Dimensional ◽  
Penalized Least Squares ◽  
Asymptotically Normal ◽  
Correct Model ◽  
Type Criterion ◽  
Simulation Results

Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by penalized least squares using various penalty functions. In this paper, an arctangent type penalty which very closely resemblesl0penalty is proposed; we call it Atan penalty. The Atan-penalized least squares procedure is shown to consistently select the correct model and is asymptotically normal, provided the number of variables grows slower than the number of observations. The Atan procedure is efficiently implemented using an iteratively reweighted Lasso algorithm. Simulation results and data example show that the Atan procedure with BIC-type criterion performs very well in a variety of settings.

scholarly journals Rapid Biochemical Methane Potential Evaluation of Anaerobic Co-Digestion Feedstocks Based on Near Infrared Spectroscopy and Chemometrics

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1460
Author(s):  
Jinming Liu ◽  
Changhao Zeng ◽  
Na Wang ◽  
Jianfei Shi ◽  
Bo Zhang ◽  
...  
Keyword(s):  
Infrared Spectroscopy ◽  
Variable Selection ◽  
Root Mean Square Error ◽  
Least Squares ◽  
Mean Square Error ◽  
Near Infrared Spectroscopy ◽  
Near Infrared ◽  
Mean Square ◽  
Biochemical Methane Potential ◽  
Methane Potential

Biochemical methane potential (BMP) of anaerobic co-digestion (co-AD) feedstocks is an essential basis for optimizing ratios of materials. Given the time-consuming shortage of conventional BMP tests, a rapid estimated method was proposed for BMP of co-AD—with straw and feces as feedstocks—based on near infrared spectroscopy (NIRS) combined with chemometrics. Partial least squares with several variable selection algorithms were used for establishing calibration models. Variable selection methods were constructed by the genetic simulated annealing algorithm (GSA) combined with interval partial least squares (iPLS), synergy iPLS, backward iPLS, and competitive adaptive reweighted sampling (CARS), respectively. By comparing the modeling performances of characteristic wavelengths selected by different algorithms, it was found that the model constructed using 57 characteristic wavelengths selected by CARS-GSA had the best prediction accuracy. For the validation set, the determination coefficient, root mean square error and relative root mean square error of the CARS-GSA model were 0.984, 6.293 and 2.600, respectively. The result shows that the NIRS regression model—constructed with characteristic wavelengths, selected by CARS-GSA—can meet actual detection requirements. Based on a large number of samples collected, the method proposed in this study can realize the rapid and accurate determination of the BMP for co-AD raw materials in biogas engineering.

Variable Selection for Partial Least-Squares Calibration of Near-Infrared Data from Orthogonally Designed Experiments

2002 ◽  
Vol 56 (3) ◽  
pp. 337-345 ◽  
Author(s):  
S. Kamaledin Setarehdan ◽  
John J. Soraghan ◽  
David Littlejohn ◽  
Daran A. Sadler
Keyword(s):  
Variable Selection ◽  
Least Squares ◽  
Partial Least Squares ◽  
Near Infrared ◽  
Designed Experiments ◽  
Selection For ◽  
Infrared Data

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.

Introduction to Penalized Least-Squares

2020 ◽  
pp. 55-120
Author(s):  
Jianqing Fan ◽  
Runze Li ◽  
Cun-Hui Zhang ◽  
Hui Zou
Keyword(s):  
Least Squares ◽  
Penalized Least Squares
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