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检验最小二乘回归计算程序舍入误差的新方法AI 解读

A new, easily applied method for examining any least-squares computer program for internal consistency is given. Only one data set is necessary, and by making appropriate transformations on these data results are given to provide an internal check on the accuracy (or consistency) of the given program. Accuracy becomes an increasing problem, of course, when the original data set is ill-conditioned. The theorems and proofs necessary to the method are presented as well as a…

相关测量误差与回归系数的最小二乘估计AI 解读

This article explores, for a set of survey conditions, the effect of correlated measurement error on the ordinary least squares estimator of the regression coefficient for a finite bivariate population, when both variables are subject to correlated measurement error. The sample estimates for some selected housing variables show that the average of the correlated measurement error components have little effect, but the simple response variance and covariance have pronounced…

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控制非正态变量均值的最优样本量与抽样间隔AI 解读

Following Duncan [3], the per hour cost of the process under the surveillance of a mean chart for controlling the mean of non-normal variables whose density function is represented by the first four terms of an Edgeworth series is obtained. The sample size and sampling interval which minimize the cost for detecting a particular shift in the process average are derived when the width of the control limits is specified. They are numerically determined for different non-normal…

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多参数情形下最大似然迭代程序的收敛问题AI 解读

In multiparameter situations there are important problems of convergence in the solution of maximum likelihood iterative equations. Convergence may be critically dependent on the initial parameter estimates employed. These problems are indicated specifically for a model of exponentially-distributed lifetimes where the reciprocal of the exponential parameter is linearly dependent on various regressor variables. A strategy is suggested based on alternative use of observed or…

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若干非标准情形下最大似然估计量的渐近性质AI 解读

Most results on the asymptotic properties of maximum likelihood estimators are for the standard cases where we observe independent and identically distributed random variables, whose distribution satisfies certain regularity conditions. In this article, similar properties are shown to hold for a class of cases where the observed random variables are not necessarily independent and identically distributed.

对数正态分布与对数正态回归的贝叶斯及非贝叶斯分析AI 解读

In this article, Bayesian and non-Bayesian methods for estimating parameters of the log-normal distribution and of log-normal regression processes are considered. Posterior distributions for parameters of interest are derived and their properties are described. With respect to point estimation, a rather broad class of estimators is defined and, relative to this class, new minimal mean square error (MSE) estimators for the median and mean of the log-normal distribution and…

位置参数的一致渐近有效估计量AI 解读

Suppose that a sample of size n from a continuous and symmetric population with an unknown parameter is given. We consider a fictitious random subsample of size k drawn from the original sample and construct the best linear estimator based on the subsample. Applying the Rao-Blackwell type argument, we get an estimator which uses the information contained in the whole sample and is supposed to be uniformly efficient for a wide class of distributions. Monte Carlo experiments…

事故发生率潜势：泊松过程多元回归分析的应用AI 解读

Various accident frequency models have appeared in the literature which predict the distribution of future accidents based on the number of past accidents. This article presents a method for deriving such distributions using several predictive criteria. It is assumed that an individual's accident experience is a Poisson process with the parameter a linear function of criterion variables. An iterative weighted least-squares procedure is used to solve the system of maximum…

计量经济学将走向何方？AI 解读

To try to chart the future of development in econometrics during the 1970's, it is useful to review the origins of the subject before World War II and the modern era in which our present body of knowledge flowered, 1940–1970. New developments should be made in computer analysis of large data banks, more complete systems, control systems, and microeconometric applications. It is likely that the future of the subject will be less tied to the United States than in the past few…

多个正态总体中最大方差的区间估计AI 解读

A procedure is given for obtaining a random width confidence interval for the largest variance of k normal populations. The determination of the sample size to achieve a preassigned confidence coefficient can be done by the use of chisquare tables only.

两个内生变量情形下结构参数 t 统计量的分布AI 解读

In this article we study the exact finite sample distribution function of a t-statistic that can be used to test hypotheses and construct confidence intervals for structural coefficients in simultaneous equations models. It is shown that the exact distribution function is equal to Student's t-distribution when one of its parameters is zero and converges to Student's t-distribution function as another of its parameters increases without bound. Computations of the exact…

参数线性但内生变量非线性的计量系统与两阶段最小二乘AI 解读

It is demonstrated that a variant of the two-stage least squares technique can be used to estimate the parameters of a nonlinear model. To do this, the reduced form equations of such models are derived and discussed; then certain problems particular to the estimation of nonlinear models are considered.

一类受噪声污染的平稳与非平稳信号的近似最优线性预测AI 解读

A technique for approximating the best linear predictor of a noise-distorted signal is presented. The technique is applicable when the signal is stationary with a spectrum which is highly concentrated around known or estimated frequencies, or when the signal is an accumulating sequence whose “spectrum” has poles at these frequencies. The noise must be stationary, but its spectrum need only be known or estimated at the above-mentioned frequencies. The time parameter is…

最小二乘估计稳定季节模式的效率AI 解读

In this article we investigate the efficiency of least squares (l.s.) in estimating a stable pattern. A model is proposed for an economic time series, which, after filtering, is a suitable basis for our investigation. The covariance structure of the disturbances is assumed known and several possible generating processes for the disturbances are considered. We contrast the variances of the l.s. estimates with those from the best linear unbiased (b.l.u.) procedure for four…

分组泊松数据的极大似然估计AI 解读

In this article, sufficient conditions are given for the existence of a unique solution of the likelihood equation which results from a grouped data sample. The necessary and sufficient conditions for the convergence of a sequence defined by the method of successive approximations to this unique solution are also given. Finally, it is shown that when the groups from an underlying Poisson distribution are connected the method of successive approximations will converge to the…

卡方分解、边际列联表分析与多维列联表期望频数估计AI 解读

A step-by-step method is presented herein for partitioning a certain kind of hypothesis H about the m-way contingency table into (a) a series of hypotheses about marginal tables formed from the m-way table by ignoring one or more of table's m dimensions; and (b) a hypothesis about independence, conditional independence, or conditional equiprobability in the m-way table. This step-by-step method facilitates both the testing of H and the calculation of , the estimated expected…

对称稳定分布的参数估计AI 解读

Building on results of an earlier article [6], estimators are suggested for the scale parameter and characteristic exponent of symmetric stable distributions, and Monte Carlo studies of these estimators are reported. The powers of various goodness-of-fit tests of a Gaussian null hypothesis against non-Gaussian stable alternatives are also investigated. Finally, a test of the stability property of symmetric stable variables is suggested and demonstrated.

序贯单样本分组符号秩对称性检验：基本程序AI 解读

Independent groups, each of N independent observations on a random variable Z, are taken sequentially with signed ranks obtained within groups. Two tests of symmetry of the parent cdf F about the origin are developed, one based on the within-group configurations of signed ranks and the other based on the within-group sums of positive signed ranks. Some properties of F are F+(z) = 1 - [1-F-(z)]k, x≥0, k>0, and F(0) = k/(k+1) where F+ and F- are respectively the conditional…

极小极大实验设计AI 解读

When an experimenter is interested in more than one parameter in the regression model and tries to obtain a design that minimizes the maximum variance of the individual regression coefficients, he is looking for a minimax design with respect to the single parameter. In this article we explicitly present the minimax s.p. designs for the ordinary polynomial regression, when the degree is ≤4. For 5≤n ≤12 we present the minimax s.p. designs obtained through a computer. These are…

多项式回归的最优实验设计AI 解读

The problem of choosing the optimal design to estimate a regression function which can be well-approximated by a polynomial is considered, and two new optimality criteria are presented and discussed. Use of these criteria is illustrated by a detailed discussion of the case that the regression function can be assumed approximately linear. These criteria, which can be considered as compromises between the incompatible goals of inference about the regression function under an…