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摘要暂缺

简单变量测量误差模型的工具变量估计AI 解读

Alternative instrumental variable estimators for the slope in the simple errors-in-variables model are discussed. The maximum likelihood estimator is derived for the model in which the error covariance is known to be zero and for the model in which the error covariance is unknown. Modified maximum likelihood estimators and randomly weighted average estimators similar to those studied by Huntsberger are discussed. The limiting distributions of the estimators are presented and…

简单测量误差模型的工具变量估计AI 解读

Alternative instrumental variable estimators for the slope in the simple errors-in-variables model are discussed. The maximum likelihood estimator is derived for the model in which the error covariance is known to be zero and for the model in which the error covariance is unknown. Modified maximum likelihood estimators and randomly weighted average estimators similar to those studied by Huntsberger are discussed. The limiting distributions of the estimators are presented and…

摘要暂缺

测量误差模型中若干估计量的性质AI 解读

The limiting behavior of estimators for several errors-in-variables models is investigated. It is assumed that an estimator of the covariance matrix of the measurement error is available. Models are delineated on the basis of the prior knowledge of the error structure. In all cases the limiting distribution of the estimators, standardized by $n^{\frac{1}{2}}$, is normal. Modifications of the estimators that guarantee finite moments and improve the small sample behavior of…

摘要暂缺

含单位根的自回归过程估计AI 解读

Let $Y_t$ satisfy the stochastic difference equation $Y_t = \sum^p_{j = 1}\eta_jY_{t - j} + e_t$ for $t = 1, 2, \cdots$, where the $e_t$ are independent identically distributed $(0, \sigma^2)$ random variables and the initial conditions $(Y_{-p + 1}, Y_{-p + 2}, \cdots, Y_0)$ are fixed constants. It is assumed the true, but unknown, roots $m_1, m_2, \cdots, m_p$ of $m^p - \sum^p_{j = 1}\eta_jm^{p - j} = 0$ satisfy $m_1 = m_2 = 1$ and $|m_j| < 1$ for $j = 3, 4, \cdots, p$.…

摘要暂缺

具有单位根的自回归时间序列估计量分布AI 解读

Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with mean 0 and variance σ2. Properties of the regression estimator of p are obtained under the assumption that p = ±1. Representations for the limit distributions of the estimator of p and of the regression t test are derived. The estimator of p and the regression t test furnish methods of…

未知对角协方差矩阵下的线性回归估计AI 解读

A method of estimating the parameters of a linear regression model when the covariance matrix is an unknown diagonal matrix is investigated. It is assumed that the observations fall into $k$ groups with constant error variance for a group. The estimation is carried out in two steps, the first step being an ordinary least squares regression. The least squares residuals are used to estimate the covariance matrix and the second step is the calculation of the generalized least…

衰减校正后的回归估计AI 解读

The limiting distribution of the regression coefficients calculated from a correlation matrix that has been corrected for attenuation is obtained. Methods of estimating the covariance matrix of the vector of regression coefficients are presented. Nonnormal regression variables and nondiagonal error matrices are considered. The procedures are illustrated with data on the socioeconomic career.

有限信息估计量一种修正的若干性质AI 解读

THE SMALL SAMPLE PROPERTIES of the estimators of parameters in a single equation of a system of equations have been investigated in several ways. Some of the many Monte Carlo studies that have been conducted are reviewed in Johnston [8]. Nagar [14] used expansions in powers of terms whose order in probability was T1, where T is the sample size, to obtain approximations of the small-sample behavior of the members of Theil's k-class estimators [18]. Basmann [4, 5], Kabe [9],…

管理者角色表现的变量测量误差分析AI 解读

A linear model with measurement error in the independent variables is considered. An errors-in-variables procedure is presented that provides estimators of the coefficients and their variances. If the dependent variable has multiple measures, the total variance of the dependent variable can be decomposed into measurement error, variance of true values explained by the true values of the independent variables and variance of true values not explained by the model. An…

摘要暂缺

嵌套误差线性模型估计的变换方法AI 解读

Two linear models with error structure of the nested type are considered. Transformations are presented by which uncorrelated errors with constant variances are obtained. The transformed observations are differences between the original observations and multiples of averages of subsets of the observations. The transformations permit the calculation of the generalized least-squares estimators and their covariance matrices by ordinary least-squares regression. Regression-type…

连接点需要估计的分段多项式回归模型拟合AI 解读

The study considers the problem of finding the least squares estimates for the unknown parameters of a regression model which consists of grafted polynomial submodels. The abscissae of the join points are a subset of the unknown parameters. Examples are given to illustrate how continuity and differentiability conditions on the model can be used to reparameterize the model so as to allow Modified Gauss-Newton fitting. A slightly generalized version of Hartley's theorem is…

伴随变量存在测量误差时的斜率估计与协方差分析AI 解读

Estimators of the slope for models with errors of observation in the explanatory variable are investigated. Estimators are developed which have a bias of smaller order and smaller mean square error than the common estimator. These estimators of slope are utilized in the analysis of covariance where the concomitant variable is measured with error. The procedure is applicable for any number of treatments or determinations per treatment. The computations are illustrated with an…

摘要暂缺

利用后分层进行估计AI 解读

Small sample estimators are developed for two post strata and compared with pooling or collapsing procedures commonly employed in practice. The estimators are not necessarily conditionally unbiased for particular sample split, but their conditional M.S.E. may be smaller than that of the common post stratified estimator. It is proven that it is always possible to construct an estimator superior to the practice of combining two post strata when one contains few sample…