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线性递归方程、协方差选择与路径分析AI 解读

By defining a reducible zero pattern and by using the concept of multiplicative models, we relate linear recursive equations that have been introduced by econometrician Herman Wold (1954) and path analysis as it was proposed by geneticist Sewall Wright (1923) to the statistical theory of covariance selection formulated by Arthur Dempster (1972). We show that a reducible zero pattern is the condition under which parameters as well as least squares estimates in recursive…

稳定分布参数的回归型估计AI 解读

A regression-type method of estimating the four parameters of a stable distribution is presented. The estimators found are consistent and approximately unbiased for moderately large sample sizes. Their efficiencies, found through a simulation study, are greater than those of most other estimators for large portions of the parameter space. Moreover, the amount of computation involved is minimal and apparently less than that needed by the methods of Paulson, Holcomb, and…

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逆相关函数的自回归与窗口估计AI 解读

The concept of the inverse correlation function of a stationary process xt was first introduced by Cleveland (1972), who also introduced the autoregressive and the window methods for estimating this function. The asymptotic distribution of the estimates provided by these two methods is derived and their asymptotic covariance structure is shown to be in accordance with a remark of Parzen (1974). The results are extended to show that the two procedures suggested by Durbin…

组内相关系数估计量的大样本方差AI 解读

A derivation is given of the large sample variance of the maximum likelihood estimator rM of the intraclass correlation coefficient p in samples of unequal size ni from a multivariate normal distribution.

有效得分检验统计量的局部功效AI 解读

The test statistic based on the efficient scores is shown to be locally biased in general. Comparisons of the local powers of this statistic, the likelihood ratio and maximum likelihood statistics reveal no uniform superiority properties. The performance of all three criteria in testing the sphericity hypothesis is examined and conditions which result in equivalence are discussed. A second example on testing for serial correlation suggests that computational simplicity may…

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极大似然估计量的一致渐近正态性AI 解读

A very general result concerning the weak consistency and uniform asymptotic normality of the maximum likelihood estimator is presented. The result proves to be of particular value in establishing uniform asymptotic normality of randomly normalized maximum likelihood estimators of parameters in stochastic processes. The only conditions imposed are certain regularity conditions on the (random) information function, easily verified in practice. Application of the result is…

样本选择偏误的最小二乘修正AI 解读

WHEN ESTIMATING REGRESSION MODELS it is very nearly always assumed that the sample is random. The recent literature has begun to deal with the problems which arise when estimating a regression model with samples which may not be random. The most general case in which one only has access to a single nonrandom sample has not been addressed since it is a very imposing problem. The case which has been addressed starts with a random sample but considers the problem of missing…

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高斯移动平均过程参数最大似然估计的不变性性质AI 解读

It is shown that the estimation procedure of Walker leads to estimates of the parameters of a Gaussian moving average process which are asymptotically equivalent to the maximum likelihood estimates proposed by Whittle and represented by Godolphin.

一类岭回归估计量的频率学派分析AI 解读

We discuss ridge regression estimators as a class, showing how six recently proposed estimators can thus be viewed, and give reasons for preferring one of these (empirical Bayes maximum likelihood estimator) to the other five. Results are based on analysis rather than simulations and on a frequentist rather than Bayesian viewpoint.

线性函数关系与联立方程中估计量分布的渐近展开AI 解读

We derive asymptotic expansions of the distributions of the maximum likelihood (ML) estimator and the ordinary least squares (OLS) estimator in a linear functional relationship model as the sample size increases infinitely. These expansions are equivalent to the asymptotic expansions of the distributions of the limited information maximum likelihood (LIML) estimator when the covariance is known to within a proportionality constant and the two-stage least squares (TSLS)…

变异系数相同但未知的两个正态总体的极大似然估计AI 解读

Maximum likelihood estimates are derived for the parameters of two normal populations with coefficients of variation equal but unknown. Formulas are provided for calculating the asymptotic variances and covariances of the estimates. The relative efficiency of the proposed mean estimator with respect to the sample mean is shown to be greater than one. The effect of departures from the assumptions of normality and of equal coefficients of variation on this relative efficiency…

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…

一类岭回归估计量的频率学派分析AI 解读

We discuss ridge regression estimators as a class, showing how six recently proposed estimators can thus be viewed, and give reasons for preferring one of these (empirical Bayes maximum likelihood estimator) to the other five. Results are based on analysis rather than simulations and on a frequentist rather than Bayesian viewpoint.

右删失观测下递增失效率分布函数的最大似然估计AI 解读

The maximum likelihood estimator of a distribution function with increasing failure rate is derived based on a set of observations subject to arbitrary right censorship. This estimator is defined everywhere on the positive real line while the Kaplan-Meier estimator may not be. The small sample properties of this estimator are indicated by results of a Monte Carlo study for the Weibull distribution.

作为近似枢轴分布的似然AI 解读

For a single-parameter curved exponential family, it is shown that the conditional distribution of the maximum likelihood estimator is the normalized likelihood function, except for a relative error proportional to inverse sample size.

平衡混合方差分析模型中的显式最大似然估计AI 解读

A result of Szatrowski, giving necessary and sufficient conditions for the existence of explicit maximum likelihood estimates for multivariate normal means and covariances with linear structure, can be applied to the problem of obtaining explicit maximum likelihood estimates in the mixed model of the analysis of variance. This application yields a simple procedure for checking whether or not explicit maximum likelihood estimates exist for the parameters in the balanced mixed…

结构化均值与协方差多元正态估计中显式解的充要条件AI 解读

The problem of finding maximum likelihood estimates for patterned means and covariance matrices in multivariate analysis is considered. Necessary and sufficient conditions are presented for the existence of explicit solutions and the obtaining of these explicit solutions in one iteration of the scoring equations from any positive definite starting point. Cases in which averaging yields the explicit maximum likelihood estimates are discussed. These results can be applied to…

多元正态均值的稳健广义贝叶斯估计与置信域AI 解读

It is observed that in selecting an alternative to the usual maximum likelihood estimator, $\delta^0$, of a multivariate normal mean, it is important to take into account prior information. Prior information in the form of a prior mean and a prior covariance matrix is considered. A generalized Bayes estimator is developed which is significantly better than $\delta^0$ if this prior information is correct and yet is very robust with respect to misspecification of the prior…

分组收入频数数据下稳定分布的统计推断AI 解读

This paper discusses inferential procedures for the family of stable distributions, when the data are tabulated in the form of interval frequencies. The estimation criteria used are minimum chi-square and multinomial maximum likelihood. In evaluating the theoretical probabilities corresponding to the intervals, use is made of the inversion theorem for characteristic functions. Chi-square tail probabilities for independent samples are pooled by means of theKolmogorov…