CONSISTENT ESTIMATION IN A LINEAR REGRESSION PROBLEM WITH RANDOM ERRORS IN COEFFICIENTS

A. I. Sakhanenko; Yu. Yu. Linke

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CONSISTENT ESTIMATION IN A LINEAR REGRESSION PROBLEM WITH RANDOM ERRORS IN COEFFICIENTS

机译：系数存在随机误差的线性回归问题的一致估计

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We consider the linear regression model in the case when the independent variables are measured with errors, while the variances of the main observations depend on an unknown parameter. In the case of normally distributed replicated regressors we propose and study new classes of two-step estimates for the main unknown parameter. We find consistency and asymptotic normality conditions for first-step estimates and an asymptotic normality condition for second-step estimates. We discuss conditions under which these estimates have the minimal asymptotic variance.

机译：当自变量被误差测量，而主要观测值的方差取决于未知参数时，我们考虑线性回归模型。对于正态分布的复制回归器，我们提出并研究了主要未知参数的新的两步估计类别。我们为第一步估计找到了一致性和渐近正态性条件，为第二步估计找到了渐近正态性条件。我们讨论了这些估计具有最小渐近方差的条件。

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《Siberian Mathematical Journal》 |2011年第4期|共16页
作者
A. I. Sakhanenko; Yu. Yu. Linke;
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正文语种 eng
中图分类数学;
关键词
linear regression; errors in independent variables; replicated regressors; dependence of variances on a parameter; two-step estimates; consistent estimate; asymptotically normal estimate;

机译：线性回归;自变量中的误差;重复回归;参数对方差的依赖性;两步估计;一致估计;渐近正态估计;

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专利

1. CONSISTENT ESTIMATION IN A LINEAR REGRESSION PROBLEM WITH RANDOM ERRORS IN COEFFICIENTS [J] . A. I. Sakhanenko, Yu. Yu. Linke Siberian Mathematical Journal . 2011,第4期

机译：系数存在随机误差的线性回归问题的一致估计
2. Asymptotically normal estimation in the linear-fractional regression problem with random errors in coefficients [J] . Yu. Yu. Linke, A. I. Sakhanenko Siberian Mathematical Journal . 2008,第3期

机译：系数具有随机误差的线性分数回归问题的渐近正态估计
3. Asymptotically optimal estimation in a linear-fractional regression problem with random errors in coefficients [J] . A. I. Sakhanenko, Yu. Yu. Linke Siberian Mathematical Journal . 2006,第6期

机译：系数具有随机误差的线性分数回归问题的渐近最优估计
4. Markov random field estimation of lost DCT coefficients in JPEG due to packet errors [C] . Yang, J., Delp, Image Processing, 2004. ICIP '04. 2004 International Conference on . 2004

机译：数据包错误导致的JPEG丢失DCT系数的马尔可夫随机场估计
5. Essays on Nonparametric Identification: Identification of Dependent Multidimensional Unobserved Variables in a System of Linear Equations Identification and Estimation for Regressions with Errors in All Variables Identification of Nonparametrically Distributed Random Coefficients in Linear Panel Data Models. [D] . Ben-Moshe, Dan. 2012

机译：关于非参数识别的论文：线性方程组中相关多维多维观测变量的识别以及线性面板数据模型中非参数分布随机系数的所有变量中所有变量均具有误差的回归估计。
6. Sieve Estimation of Constant and Time-Varying Coefficients in Nonlinear Ordinary Differential Equation Models by Considering Both Numerical Error and Measurement Error [O] . Hongqi Xue, Hongyu Miao, Hulin Wu -1

机译：恒的筛估计和时变系数的非线性常微分方程模型同时考虑数值误差和测量误差
7. Using stochastic prior information in consistent estimation of regression coefficients in replicated measurement error model [O] . Singh Sukhbir, Jain Kanchan, Sharma Suresh 2012

机译：在复制的测量误差模型中使用随机先验信息一致估计回归系数
8. Strongly Consistent Estimates of Regression Coefficients when the Errors are not Independently and Identically Distributed [R] . Wu, Y. 1986

机译：当误差不是独立且相同分布时，回归系数的非常一致的估计

CONSISTENT ESTIMATION IN A LINEAR REGRESSION PROBLEM WITH RANDOM ERRORS IN COEFFICIENTS

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