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通过最大值随机变量的分布识别参数AI 解读

Summary Under what conditions does the distribution of the maximum of a set of independent random variables uniquely determine the distributions of the component random variables? In the univariate case, a sufficient condition is that for every pair of distinct densities in the family of possible densities, one density converges to zero infinitely faster than the other, as x → ∞. Hence, the distribution of max {X i, i = 1, ..., n} when X i has the distribution N(μi, σ2 i),…

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两阶段最小二乘：应沿哪个方向最小化残差？AI 解读

A structural equation in a complete system may be written with the coefficient of one endogenous variable as unity and the coefficients of the other endogenous variables as parameters. To estimate these parameters two-stage least squares is usually applied by minimizing residuals in the direction of the first variable. In this paper, when there is one such parameter, that procedure is compared with adapting two-stage least squares to minimize residuals in the direction of…

两阶段最小二乘：应沿哪个方向最小化残差？AI 解读

A structural equation in a complete system may be written with the coefficient of one endogenous variable as unity and the coefficients of the other endogenous variables as parameters. To estimate these parameters two-stage least squares is usually applied by minimizing residuals in the direction of the first variable. In this paper, when there is one such parameter, that procedure is compared with adapting two-stage least squares to minimize residuals in the direction of…

不同参数序列下联立方程估计量分布的渐近展开AI 解读

The distributions of the LIML and TSLS estimates of the coefficient of an endogenous variable in a single equation can be approximated by asymptotic expansions. This paper relates the expansions in terms of the noncentrality parameter and the sample size going to infinity, the noncentrality parameter going to infinity with the sample size held fixed, and the standard deviation of the disturbance going to zero (small-o). 1. INTRODUCriON RECENTLY, ASYMPTOTIC EXPANSIONS of the…

联立系统中单个方程系数估计量的分布及其渐近展开AI 解读

T. W. Anderson, Takamitsu Sawa, Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions, Econometrica, Vol. 44, No. 6 (Nov., 1976), p. 1329

控制问题中最小二乘估计统计性质的实验结果AI 解读

The statistical properties of the certainty equivalence control rule and of the least squares estimates generated by this rule are examined experimentally in a linear model with two unknown parameters. It is found that the least squares certainty equivalence rule converges to its true value with probability one and is asymptotically efficient, having an asymptotic distribution with a variance as small as any other strongly consistent rule. However, while a linear combination…

线性函数关系估计：近似分布及与计量联立方程的联系AI 解读

Summary When both variables are subject to error, a straight line may be fitted by minimizing the sum of squared distances of the observed points to the line. Approximate distributions of the slope of this line and of the angle it makes to one axis are given when the errors are normal, uncorrelated, and with equal variances. These distributions and corresponding ones for the line fitted by ordinary least squares are found by making the model equivalent to a model of…

正态线性回归中最小二乘估计的强相合性AI 解读

In the usual linear regression model the sample regression coefficients converge with probability one to the population regression coefficients when the dependent variables are normally distributed and the inverse of the second-order moment matrix of the independent variables converges to the zero matrix.

移动平均残差自回归过程及线性结构协方差矩阵的最大似然估计AI 解读

The autoregressive process with moving average residuals is a stationary process $\{y_t\}$ satisfying $\sum^p_{s = 0} \beta_sy_{t - s} = \sum^q_{j = 0} \alpha_j\nu_{t - j}$, where the sequence $\{\nu_t\}$ consists of independently identically distributed (unobservable) random variables. The distribution of $y_1,\cdots, y_T$ can be approximated by the distribution of the $T$-component vector $\mathbf{y}$ satisfying $\sum^p_{s = 0} \beta_s\mathbf{K}_s\mathbf{y} = \sum^q_{j = 0} \alpha_j\mathbf{J}_j\mathbf{v}$…

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联立方程系统中系数的有限信息最大似然估计分布的渐近展开AI 解读

An asymptotic expansion is made of the distribution of the limited information maximum likelihood estimate of the coefficient of one endogenous variable in an equation with two endogenous variables when the coefficient of the other endogenous variable is prescribed to be unity. The equation is one of a system of simultaneous equations, and all the predetermined variables in the system are assumed to be exogenous. The expansion in terms of the noncentrality parameter, which…

学生化分类统计量 W 的分布渐近展开AI 解读

The classification statistic $W$ is used to classify an observasion as coming from one of two multivariate normal populations with common covariance matrix and different means when these parameters are estimated from two samples, one from each population. The distribution of $W$ depends on the Mahalanobis distance between the populations, $\alpha$. When the sample sizes approach infinity, the limiting distribution of $(W - \frac{1}{2}\alpha)/\alpha^{\frac{1}{2}}$ is the…

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具有线性结构的协方差矩阵的渐近有效估计AI 解读

One or more observations are made on a random vector, whose covariance matrix may be a linear combination of known symmetric matrices and whose mean vector may be a linear combination of known vectors; the coefficients of the linear combinations are unknown parameters to be estimated. Under the assumption of normality, equations are developed for the maximum likelihood estimates. These equations may be solved by an iterative method; in each step a set of linear equations is…

针对赤道型与双峰备择的方向随机性检验AI 解读

Tests of randomness of directions in three-dimensional space or equivalently tests of uniform distribution of points on the unit sphere are treated. One test is against alternatives, which concentrate probability density near an equator, and the other is against alternatives which concentrate probability density near opposite poleθ in each case the poles are unspecified. The tests are based on the latent roots of the matrix of sums of squares and cross-products of the…

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将实验数据用于生产过程绩效预测的若干统计问题AI 解读

The performance of a production process is characterized by the quantity and quality of the output; it is affected by factors of production, such as conditions of the process and quantities of inputs. In experimentation where the factors are controlled, we assume a bivariate linear regression model with quantity and quality of output as dependent variates. In operation where quality of output is controlled by adjusting one of the factors, another regression model is used in…

将实验数据用于预测生产过程表现的若干统计问题AI 解读

The performance of a production process is characterized by the quantity and quality of the output; it is affected by factors of production, such as conditions of the process and quantities of inputs. In experimentation where the factors are controlled, we assume a bivariate linear regression model with quantity and quality of output as dependent variates. In operation where quality of output is controlled by adjusting one of the factors, another regression model is used in…