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回归分析中扰动估计的进一步讨论AI 解读

For the well-known general linear model Theil has recently developed the so-called best linear disturbance estimates with a covariance matrix equal to σ2 I. In this article we give a slightly different formulation of his problem which may give us some more insight in this estimation procedure. An important check on the computations of these estimates is given, as well as a comparison of these estimates with the commonly used least-squares estimates. For some special cases…

用于计量经济分析的数据季节调整AI 解读

An earlier paper [3] provides axioms for the seasonal adjustment of economic time series. Seasonally adjusted data should be minimum variance, unbiased, and linear in an appropriate sense. These axioms yield a unique method for seasonal adjustment. The seasonally adjusted data may be obtained by an application of ordinary least squares regression.1 The problem of seasonal adjustment of economic time series in [3] is not the same as the problem of seasonal adjustment of data…

多元分析中求解离散程度矩阵函数零点的算法AI 解读

This paper is devoted to a discussion of an iterative procedure for obtaining the maximum likelihood estimator of the covariance matrix for multivariate experiments in which measurements on certain components of a normal vector random variable are intentionally omitted in corresponding subgroups of the experimental units. The proposed algorithm, which is based on the Newton-Raphson method, is outlined in detail in Section 5. A special design is included to illustrate the…

基于顺序统计量的柯西分布位置估计AI 解读

In a recent paper in this Journal, Rothenberg, Fisher and Tilanus [1] discuss a class of estimators of the location parameter of the Cauchy distribution, taking the form of the arithmetic average of a central subset of the sample order statistics. They show that the average of roughly the middle quarter of the ordered sample has minimum asymptotic variance within this class, and that asymptotically it eliminates about 36 per cent of the efficiency loss of the median (the…

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…

部分调整与适应性预期模型误设造成的小样本偏差AI 解读

The “partial adjustment” and “adaptive expectations” models are simply special cases of a more general model. This fact has not been commonly recognized by investigators who have used one or the other of these two models in empirical economic research. An examination of the results of small sample experiments shows that the bias in the estimated regression coefficients and the estimated mean lag which occurs when either one of the models is fitted by least squares to data…

可靠性函数的最大似然与最佳无偏估计的小样本效率AI 解读

The paper presents the results of an inquiry concerning the small sample relative efficiency of maximum likelihood and best unbiased estimators of reliability functions of one-unit systems. Three cases are considered: The Poisson, exponential, and normal (standard deviation known). Two kinds of relative efficiency functions are studied. The first kind consists of the common ratio of the Cramér-Rao lower bound of the variances of unbiased estimators, to the mean-square-error…

由同一指数分布的 k 个部件构成的系统可靠性点估计AI 解读

Minimum variance unbiased estimators of reliability are developed for a series, parallel, and standby redundant system where the components are from a single exponentially distributed population. It is assumed that sampling information has been censored with respect to number of failures or test time.

论稳健统计程序AI 解读

This paper discusses a procedure for finding robust estimators of the location parameter of symmetric unimodal distributions. The estimators are based on robust rank tests and the methods used are applicable to other one parameter problems. To every density function there corresponds an asymptotically most powerful rank test (a.m.p.r.t.). For a set , of density functions the maximin rank test, R, maximizes the minimum limiting Pitman's efficiency of R relative to the…

具有平稳误差的多元回归AI 解读

A practical computing technique is presented for the joint estimation of regression coefficients and the error spectrum in regression problems with stationary errors. In problems where unweighted least squares is not efficient, the procedure gives an estimate approaching the minimum variance linear unbiased estimate. Whether unweighted least squares is nearly efficient or not efficient, the procedure, in general, gives a much closer estimate of the covariance matrix of the…

修订后美国国民账户中的统计差额AI 解读

As is well known, the U. S. national accounts contain a “Statistical Discrepancy” which serves to reconcile estimates of GNP from the product and from the income side. While the Discrepancy is a measure only of overall consistency rather than of error, its magnitude and pattern over time do give some indication of the quality of the national accounts data. In the past, the Statistical Discrepancy has not always behaved as a quantitatively unimportant random error term—a…

减弱真实大观测值影响的总体均值估计量AI 解读

An estimator, , of μ is investigated. This estimator is formed by replacing all sample values larger than a predetermined cutoff point t by the value of t itself. A proof is given that a region for t exists for certain common distributions such that MSE is smaller than An example is presented which demonstrates the wide range of cutoff points that can be chosen which still result in a gain.

两个随机序变量分布的最大似然估计AI 解读

The maximum likelihood estimates and Ĝ of two distribution functions F and G are found, subject to the restrictions that for all x and that and Ĝ are of the discrete type. Random samples x 1, ···, x m and y 1, ···, y n are taken from the respective distributions and these m+n values are ordered according to magnitude, with x's before y's in cases of equality. These n+m values are divided into a number of “strings” as follows. The first string ends after the y value that is…

高斯—马尔可夫定理的一个推广AI 解读

This paper contains a generalization of the Gauss Markov Theorem based on the properties of the generalized inverse of a matrix as defined by Penrose. A minimum variance vector estimate of a parameter vector x is given for the linear model of less than full rank. Since linear unbiased estimates may not always exist for this case the unbiased constraint is replaced by the more general constraint that the norm is minimized.

串联系统与并联系统可靠性函数的无偏及最大似然估计AI 解读

The bias and mean-square-error functions of the maximum likelihood and best unbiased estimator of reliability functions are derived. Information is available on the operation of subsystems connected in series or in parallel. The Poisson and the exponential cases are considered.

加速折旧采用的学习函数估计AI 解读

The Revenue Act of 1954 permitted entrepreneurs for the first time to make use of the double declining balance (DDB) and sum of the year's digits (SYD) methods of depreciation in place of the customary straight line method (SL). The tax advantages from using such methods are well known.1 In spite of these advantages, however, the accelerated methods in many cases appear to have been adopted only slowly over the years. Clearly any attempt to determine the effect on investment…

由 Student 分布刻画卡方分布AI 解读

It is known that if X 0, X 1 are independent random variables identically distributed according to the chi square distribution with n degrees of freedom then the random variable follows the Student distribution with n degrees of freedom. But the chi square distribution can not be characterized by this property, because there exist pairs X 0, X 1 of independent positive random variables identically distributed according to distributions differing from chi square, and for…

列联表卡方检验的功效AI 解读

The general theory of the asymptotic power of chi square tests requires the evaluation of a non-centrality parameter which is expressed as a vector-matrix vector product. This parameter is evaluated for two of the models associated with r × c contingency tables. This permits the power of such tests to be approximated on a large sample basis. Further considered are some implications of these results for sample design problems.

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