Estimation of Error Variance in Regularized Regression Models via Adaptive Lasso

被引:4
|
作者
Wang, Xin [1 ]
Kong, Lingchen [1 ]
Wang, Liqun [2 ]
机构
[1] Beijing Jiaotong Univ, Dept Appl Math, Beijing 100044, Peoples R China
[2] Univ Manitoba, Dept Stat, Winnipeg, MB R3T 2N2, Canada
基金
中国国家自然科学基金;
关键词
high-dimensional linear model; variance estimation; natural adaptive lasso; mean squared error bound; regularized regression; NONCONCAVE PENALIZED LIKELIHOOD; VARIABLE SELECTION;
D O I
10.3390/math10111937
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Estimation of error variance in a regression model is a fundamental problem in statistical modeling and inference. In high-dimensional linear models, variance estimation is a difficult problem, due to the issue of model selection. In this paper, we propose a novel approach for variance estimation that combines the reparameterization technique and the adaptive lasso, which is called the natural adaptive lasso. This method can, simultaneously, select and estimate the regression and variance parameters. Moreover, we show that the natural adaptive lasso, for regression parameters, is equivalent to the adaptive lasso. We establish the asymptotic properties of the natural adaptive lasso, for regression parameters, and derive the mean squared error bound for the variance estimator. Our theoretical results show that under appropriate regularity conditions, the natural adaptive lasso for error variance is closer to the so-called oracle estimator than some other existing methods. Finally, Monte Carlo simulations are presented, to demonstrate the superiority of the proposed method.
引用
收藏
页数:19
相关论文
共 50 条
  • [1] A STUDY OF ERROR VARIANCE ESTIMATION IN LASSO REGRESSION
    Reid, Stephen
    Tibshirani, Robert
    Friedman, Jerome
    [J]. STATISTICA SINICA, 2016, 26 (01) : 35 - 67
  • [2] Estimation of error variance via ridge regression
    Liu, X.
    Zheng, S.
    Feng, X.
    [J]. BIOMETRIKA, 2020, 107 (02) : 481 - 488
  • [3] Error variance function estimation in nonparametric regression models
    Alharbi, Yousef F.
    Patili, Prakash N.
    [J]. COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2018, 47 (05) : 1479 - 1491
  • [4] Bootstrap estimation of the variance of the error term in monotonic regression models
    Sysoev, O.
    Grimvall, A.
    Burdakov, O.
    [J]. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 2013, 83 (04) : 625 - 638
  • [5] Multiple Change-Points Estimation in Linear Regression Models via an Adaptive LASSO Expectile Loss Function
    Gabriela Ciuperca
    Nicolas Dulac
    [J]. Journal of Statistical Theory and Practice, 2022, 16
  • [6] Multiple Change-Points Estimation in Linear Regression Models via an Adaptive LASSO Expectile Loss Function
    Ciuperca, Gabriela
    Dulac, Nicolas
    [J]. JOURNAL OF STATISTICAL THEORY AND PRACTICE, 2022, 16 (03)
  • [7] Locally adaptive semiparametric estimation of the mean and variance functions in regression models
    Chan, David
    Kohn, Robert
    Nott, David
    Kirby, Chris
    [J]. JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, 2006, 15 (04) : 915 - 936
  • [8] Adaptive Lasso for vector Multiplicative Error Models
    Cattivelli, Luca
    Gallo, Giampiero M.
    [J]. QUANTITATIVE FINANCE, 2020, 20 (02) : 255 - 274
  • [9] Subspace Clustering via Variance Regularized Ridge Regression
    Peng, Chong
    Kang, Zhao
    Cheng, Qiang
    [J]. 30TH IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR 2017), 2017, : 682 - 691
  • [10] Error variance estimation in semi-functional partially linear regression models
    Aneiros, German
    Ling, Nengxiang
    Vieu, Philippe
    [J]. JOURNAL OF NONPARAMETRIC STATISTICS, 2015, 27 (03) : 316 - 330