A Regularized Estimator For Linear Regression Model With Possibly Singular Covariance

Hoang H. S.; Baraille R.

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A Regularized Estimator For Linear Regression Model With Possibly Singular Covariance

机译：可能具有奇异协方差的线性回归模型的正则估计

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摘要

A regularized estimator is proposed for regression models in the case where the covariances may be singular. Conditions guaranteeing proximity of a regularized estimator to the optimal estimator are obtained by appropriate choice of regularization parameters by allowing a prescribed level of uncertainty. A simple Monte-Carlo simulation study is reported to highlight some aspects and performance of the proposed approach.

机译：在协方差可能是奇异的情况下，建议对回归模型使用正则估计量。通过允许规定水平的不确定性，通过适当选择正则化参数来获得保证正则化估计量与最佳估计量接近的条件。据报道，一项简单的蒙特卡洛模拟研究突出了该方法的某些方面和性能。

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《IEEE Transactions on Automatic Control》 |2013年第1期|236-241|共6页
作者
Hoang H. S.; Baraille R.;
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作者单位

H.Hoang is with SHOM/CMO, 42 Avenue Gaspard Coriolis 31100 Toulouse, France.;

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正文语种 eng
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关键词
Convergence; Eigenvalues and eigenfunctions; Estimation error; Mathematical model; Stability analysis; Vectors; Covariance matrix; LMS algorithm; linear regression system; parameter estimation; regularization;

机译：收敛;特征值和特征函数;估计误差;数学模型;稳定性分析;向量;协方差矩阵LMS算法;线性回归系统参数估计;正规化;

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专利

1. Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors [J] . ?tulajter Franti?ek Applications of mathematics . 1991,第2期

机译：具有协方差平稳误差的回归模型中线性和二次最小二乘估计的一致性
2. The best linear unbiased estimator in a singular linear regression model [J] . Jibo Wu, Chaolin Liu Statistical papers . 2018,第3期

机译：单数线性回归模型中最好的线性无偏估计
3. Large deviations of the correlogram estimator of the random noise covariance function in the nonlinear regression model [J] . Ivanov Alexander, Kozachenko Yuriy, Moskvychova Kateryna Communications in Statistics . 2021,第16a18期

机译：非线性回归模型中随机噪声协方差函数的相关性估计的大偏差
4. A Technique for Estimator Densities applied to Exponential Regression, Nonlinear Regression models and Biochemical Titration Curves [C] . Peter Hingley World Congress on Engineering . 2008

机译：应用于指数回归，非线性回归模型和生物化学滴定曲线的估计密度技术
5. Finite sample performance of nonparametric regression estimators: The case of additive and parametric covariance models. [D] . Yang, Ke. 2006

机译：非参数回归估计量的有限样本性能：加性和参数协方差模型的情况。
6. Constrained S-estimators for linear mixed effects models with covariance components [O] . Inna Chervoneva, Mark Vishnyakov -1

机译：具有协方差分量的线性混合效果模型的受限S估算器
7. Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors [O] . František Štulajter 1991

机译：具有协方差静止误差的回归模型中线性和二次最小二乘估计的一致性

A Regularized Estimator For Linear Regression Model With Possibly Singular Covariance

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