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一致改进估计量的构造AI 解读

A new way of constructing uniformly better estimators (in the sense of minimum variance) from two independent unbiased estimators is presented. The problem of weighting estimators, when the ratio of their variances is unknown, is not straightforward. Yet this problem is particularly important in the recovery of inter-block information in balanced incomplete blocks. The theorem given in this paper suggests a simple method of constructing “better” estimators. The theorem has…

典型三方程情形下广义经典线性估计量的精确有限样本密度函数札记AI 解读

In this article some leading results of a mathematical investigation of exact finite sample distributions of GCL estimators are given. These results pertain to the distributions of estimators of coefficients appearing in econometric systems of three structural equations. The results show that the general forms of exact distributions derived for coefficient estimators in two-equation systems re-appear in the corresponding cases of three equations systems.

经济时间序列中季节变动的估计AI 解读

The problem of estimating the seasonal component in an economic time series is discussed and it is pointed out that the effects of any moving average operator on the seasonal component may be easily reversed so that one may use any suitable operator to remove the trend. The computational procedure is to estimate the seasonal index for the trend free series and to convert this index into a seasonal index for the original series by taking 12 term moving averages of this series…

有界随机变量和的概率不等式AI 解读

Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr {S – ES ≥ nt} depend only on the endpoints of the ranges of the summands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U…

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次序统计量的不相关线性函数AI 解读

In this paper the correlation between the mean and certain linear functions of Order Statistics are obtained for samples from any population and the results for the symmetrical population are derived therefrom. The results obtained in this paper answer in part a question raised by Ostle and Steck in their 1959 paper [2].

三种不等概率不放回抽样程序AI 解读

In this paper we consider three well-known procedures of unequal probability sampling without replacement. Using an asymptotic approach, Hartley and Rao [3] have obtained compact expressions for variance and estimated variance for one of these procedures. Here we develop formulae for variance and estimated variance for the other two procedures, using their asymptotic approach. It is shown that for large and moderate size populations the three procedures have almost the same…

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抽样调查中的比率估计偏差AI 解读

Sample survey data are commonly expressed by the ratio mean r = y/x, where both y and x are random variables, each the sum of a survey variable. Most commonly, x is simply the sample size and r the sample mean. Simplicity of computing and presenting this mean gives it considerable advantages, particularly in multi-purpose surveys. Though consistent, it is not an unbiased estimator. Our empirical investigations, set in a theoretical framework, show that the bias in most…

采用 Probit 与 Logit 变换的线性假设检验之渐近功效AI 解读

The statistic for testing the fit of a linear model, or the statistic for testing a linear hypothesis under the model, when using probits or logits, has a central χ2-distribution for large samples if the null hypothesis is true. If it is not true, the test statistic has, asymptotically, a non-central χ2-distribution with a non-centrality parameter that depends on the alternative hypothesis, the model, and the transformation. Non-Centrality parameters associated with tests of…

多项分布各类别概率相等的序贯检验AI 解读

For testing the hypothesis that all the categories in a multinomial distribution are equally likely, a sequential test is proposed which at each stage of the sampling observes whether the observation falls in the set of categories containing the largest number of earlier observations. It rejects the hypothesis if at too many stages the observation does fall in that set of categories. The properties of the test are discussed.

利用相关序列进行时间序列插值AI 解读

The construction of most comprehensive economic time series involves the estimation of some components for some dates by interpolation between values (“benchmarks”) for earlier and later dates. This is often done by using a related series known for all relevant dates. In practice, the bulk of such interpolation uses only a single related series, its values for only three dates—the interpolation date, one prior date, and one later date—and the values of the given series for…

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多项分布各类别概率相等的序贯检验AI 解读

For testing the hypothesis that all the categories in a multinomial distribution are equally likely, a sequential test is proposed which at each stage of the sampling observes whether the observation falls in the set of categories containing the largest number of earlier observations. It rejects the hypothesis if at too many stages the observation does fall in that set of categories. The properties of the test are discussed.

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使用 Probit 与 Logit 变换的线性假设检验渐近功效AI 解读

The statistic for testing the fit of a linear model, or the statistic for testing a linear hypothesis under the model, when using probits or logits, has a central χ2-distribution for large samples if the null hypothesis is true. If it is not true, the test statistic has, asymptotically, a non-central χ2-distribution with a non-centrality parameter that depends on the alternative hypothesis, the model, and the transformation. Non-Centrality parameters associated with tests of…

抽样调查中的比率估计偏差AI 解读

Sample survey data are commonly expressed by the ratio mean r = y/x, where both y and x are random variables, each the sum of a survey variable. Most commonly, x is simply the sample size and r the sample mean. Simplicity of computing and presenting this mean gives it considerable advantages, particularly in multi-purpose surveys. Though consistent, it is not an unbiased estimator. Our empirical investigations, set in a theoretical framework, show that the bias in most…

两阶段抽样中的若干比率型估计量AI 解读

Several ratio-type estimators in two-phase sampling are presented. One of them is an unbiased estimate and follows direct from the one given by Hartley and Ross for single phase sampling. The paper gives the variances of each of these estimates and discusses the efficiency of the unbiased estimate as compared to the biased estimates. Lastly, the paper gives a numerical illustration and discusses the efficiency of two-phase sampling with respect to single phase sampling under…

后分层加权估计量的方差AI 解读

A straightforward procedure is presented which uses the variance formula of a simple estimator to obtain an approximate formula for the variance of a post-stratified estimator. The approximation is the well-known one for the variance of a ratio estimator. The technique is applied to samples which have been selected in stratified and multistage designs and can be extended to other ratio estimators.

抽样调查中的回归分析AI 解读

Models are proposed as a basis for unbiased and biased estimation from sample survey data of a regression relation. Unbiased estimates of the variances and covariances of estimates of the regression coefficients are obtained for certain cases but do not appear to exist for all cases. It is suggested that past surveys, conducted mostly to obtain efficiently estimates of means and totals, be analyzed to yield estimates of regression relations, to obtain information needed in…

Kendall τ与平均τ的简便计算及含基准排序平均τ的抽样分布AI 解读

Calculational short cuts for Kendall's tau and average tau and for Hays' average tau with a criterion ranking (τC ) are shown. The short cuts are based mainly on counting “inversions” in the ordering of n objects by a given judge, and summing over m judges, rather than counting agreements for a given object-pair and summing over object-pairs. The sum of the number of inversions thus counted for τC has a limiting normal distribution under the null hypothesis. From this is…

属性寿命试验中的若干实验设计问题AI 解读

Many life testing procedures which have been developed involve continuous monitoring of the items under test. In storage deterioration problems, as an example, the failure of items can only be ascertained by means of inspection. Continuous observation, in these cases, is either not possible or not feasible. This paper is concerned with design problems related to the choice of the number and timing of inspections. A general class of survival functions is investigated and…