Estimation of the mean of a univariate normal distribution when the variance is not known

Dmitry Danilov

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Estimation of the mean of a univariate normal distribution when the variance is not known

机译：当方差未知时估计单变量正态分布的均值

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We consider the problem of estimating the first k coefficients in a regression equation with k + 1 variables. For this problem with known variance of innovations, the neutral Laplace weighted-average least-squares estimator was introduced in Magnus (2002). We generalize this estimator to the case where the unknown variance is estimated by least squares and find that main properties of the Laplace estimator only change marginally. Therefore we recommend the neutral Laplace estimator to be used in practice.

机译：我们考虑用k + 1变量估计回归方程中前k个系数的问题。对于具有已知创新差异的此问题，Magnus（2002）引入了中性拉普拉斯加权平均最小二乘估计器。我们将该估计器推广到最小方差估计未知方差的情况，并发现拉普拉斯估计器的主要属性仅发生少量变化。因此，我们建议在实践中使用中性拉普拉斯估计量。

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来源
《The econometrics journal》 |2005年第3期|p.277-291|共15页
作者
Dmitry Danilov;
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作者单位

EURANDOM, Technical University of Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;

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原文格式 PDF
正文语种 eng
中图分类 f;
关键词
regression; pretest; laplace estimator;

机译：回归;前测;拉普拉斯估计;

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1. Estimation of the Mean and Variance of a Univariate Normal Distribution Using Least-Squares via the Differential and Integral Techniques [J] . C. R. Kikawa, M. Y. Shatalov, P. H. Kloppers International Journal of Probability and Statistics . 2015,第2期

机译：通过微分和积分技术使用最小二乘估计单变量正态分布的均值和方差
2. Modified Three-Stage Sampling for Fixed-Width Interval Estimation of the Common Variance of Equicorrelated Normal Distributions [J] . Shyamal K. De Sequential analysis . 2014,第1期

机译：修正三阶段采样法，对等相关正态分布的共同方差进行定宽区间估计
3. On Two-Stage Sampling for Fixed-Width Interval Estimation of the Common Variance of Equi-Correlated Normal Distributions [J] . Dina M. Haner, Shelemyahu Zacks Sequential analysis . 2013,第3期

机译：等阶段正态分布共同方差固定宽度区间估计的两阶段抽样
4. The Stochastic Imperfection Method of Sheet Space Structure Based On Truncated Univariate Normal Distributions [C] . Tian-jiao JIN, Xiao-ming GUO International Conference on Material Science and Environmental Engineering . 2014

机译：基于截短的单变量正态分布的薄板空间结构随机缺陷方法
5. Estimation of the parameters of skew normal distribution by approximating the ratio of the normal density and distribution functions. [D] . Dey, Debarshi. 2010

机译：通过近似正态密度和分布函数的比率来估计偏正态分布的参数。
6. OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE [O] . Xianchao Xie, S. C. Kou, Lawrence Brown -1

机译：具有二次方差分布族的平均参数的最佳收缩估计
7. Estimation of the mean of a univariate normal distribution when the variance is not known [O] . Danilov, DL Dmitry 2005

机译：当方差未知时估计单变量正态分布的均值
8. CONTRIBUTIONS TO UNIVARIATE OR MULTIVARIATE ANALYSIS OF VARIANCE WITH FIXED EFFECTS, NORMAL OR NONNORMAL RANDOM EFFECTS, AND NORMAL ERROR [R] . S. N. Roy, Whitfield Cobb 1958

机译：对具有固定效应，正常或非正常随机效应和正常错误的方差的单因素或多元分析的贡献

Estimation of the mean of a univariate normal distribution when the variance is not known

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