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若干圆形误差分位数估计量的渐近性质AI 解读

Quantiles of circular error, of which the CPE (circular probable error) is a special case, are of importance in the evaluation of ballistic missile systems. In these applications, a quantile of circular error is the radius, R, of a circle centered at (0, 0) above which lies a specified proportion, P, of the bivariate normal probability distribution. For this distribution, R may be estimated by substituting estimates for parameters in the integral equation defining R and…

多元正态分布的置信区域、预测区域与容忍区域AI 解读

Formulas for confidence, prediction, and tolerance regions for the multivariate normal distribution for the various cases of known and unknown mean vector and covariance matrix are assembled for easy reference in this expository paper. Tables are provided for the bivariate case.

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均匀分布及相关分布相等性的检验AI 解读

Let X 1, …, Xk be k stochastically independent random variables and let Xi have the uniform distribution on the interval from 0 to θ i , i = 1, …, k. The power function of the likelihood ratio test is found for the problem of testing {H 0: θ1 = … = θ k θ0, θ0 specified; H 1: θ i ≠ θ0 for at least one i, i = 1, …, k}, and ump possibilities are investigated. For the problem of testing {H 0: θ1 = θ2, common value unspecified; H 1: θ1 ≠ θ2}, the power function of the likelihood…

季节调整的不同公理化方案AI 解读

The Jorgenson and Lovell axiomatizations of the process of seasonal adjustment are contrasted in this paper. It is argued that dummy variables rather than data subject to prior seasonal adjustment should be employed when time series are utilized in estimating the parameters of a linear economic model.

Wilcoxon 检验、并列值与计算机计算AI 解读

In testing for equality of distribution in two unpaired samples with ordered categorical data or data with many ties, the two sample Wilcoxon average rank test is attractive. Unfortunately, the null distribution of the statistic depends upon the pattern of ties and is generally difficult to compute. In an attempt to improve existing approximations, moments through order four are derived. It is regretted that in small to moderate sample sizes, no consistent improvement over…

条件正态回归模型AI 解读

A relatively complete discussion is provided for the limiting distributions of certain sample correlation coefficients and sample correlation ratios. It is assumed for the random variables X and Y that the conditional distribution of Y, given X = x, is multivariate normal with a constant, but unknown, covariance matrix and that the distribution of X has finite fourth moments. The sample coefficients are then based on a random sample from the (X, Y)-distribution. For the case…

Behrens–Fisher 问题中两种检验程序的置信区间比较AI 解读

The procedures of Scheffé [4] and Welch [5] for testing equality of means of two normal populations are compared according to the expected lengths of the confidence intervals they yield, and a criterion is developed for deciding which of the two methods is better in any given situation. An expression for the expected length of the confidence interval for the Scheffé procedure was developed by Scheffé. Because of the asymptotic series nature of the Welch procedure, in this…

关联度量 Gamma 的样本统计量分布AI 解读

Random sampling experiments were performed to determine whether Goodman and Kruskal's asymptotic theory (2) for the sample version (G) of the measure of association Gamma (γ) is applicable to small samples. First, the asymptotic theory was checked against the results obtained with a series of 5 × 5 population cross classifications with values of γ covering the full range. For samples of size fifty, the tails of the distribution of (G — γ)/σ corresponded closely to the tails…

一般线性假设检验的敏感度比较AI 解读

The expected significance level (ESL) of a test, proposed by Dempster and Schatzoff (4) as a criterion for comparing sensitivities of competing test statistics, is defined as the expected value of the observed significance level under a simple alternative hypothesis. For example, the ESL of a lower tailed test of the hypothesis H 0: X∼F (x) against H 1: X∼G (x) is given by ñF(x)dG(x). In this paper, the sensitivities of several proposed tests of the general linear hypothesis…

具有准线性残差的随机过程振幅谱估计札记AI 解读

It is shown that when a deterministic signal is observed in quasi-linear noise (herein defined), the usual estimate of the signal amplitude spectrum for a finite time interval converges uniformly and exponentially fast in probability to this spectrum as the length of the time interval becomes infinite. When the limiting amplitude spectrum exists, the estimate tends to this function exponentially fast but no longer uniformly, in general.

不等概率不放回抽样中两指定单位共同入样概率的精确公式AI 解读

Given a population of N units, it is required to draw a sample of n distinct units in such a way that the probability π i , (i = 1, …, N) for the ith unit to be in the sample is proportional to its ‘size’ xi. One way to achieve this is as follows: The N units in the population are listed in a random order and their xi are cumulated and a systematic selection of n elements from a “random start” is then made on the cumulation. The mathematical theory associated with this…

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截断 Logistic 分布次序统计量的精确矩与乘积矩AI 解读

The order statistics of an arbitrary size random sample of variates which originate from a logistic distribution with an arbitrary degree of truncation, both one-sided and two-sided, are considered. A general expression for the product moments of the order statistics in the onesided truncation case is derived by application of a formula obtained from the Euler Transformation. A generalization of this formula is used to obtain an expression for the product moments of the…

利用回归技术分解月度全国零售贸易估计的地区结果AI 解读

A common problem in sample estimation is the one of producing estimates for parts of the original universe (these parts are variously referred to in the literature as domains, subuniverses or subpopulations and may be defined in terms of areas or other characteristics). A technique is presented for producing these part-estimates when ratio or regression estimates are involved. This technique is used to produce estimates of retail trade for areas such as States, geographic…

基于等容量小样本的两个正态总体共同均值无偏估计AI 解读

Given two independent simple random samples of equal size from two normal distributions, N(μ, σ2 i ) (i = 1, 2), the problem is to estimate the common mean μ, — ∞ < μ, < ∞. The variance ratio ρ = σ2 2/σ2 1 is unknown. Two classes of randomized unbiased estimators are studied. Let (, S 1, S 2) denote the sample means and sums of squares of deviations. For both classes of estimators a two-sided F-test is performed. If F = S 2/S 1 falls in the interval (1/ρ, ρ), where ρ is a…

多元线性回归中最小二乘与向量相关的一个定理AI 解读

This paper shows that the least-squares estimate of the matrix of coefficients in a multivariate linear regression model maximizes the squared vector correlation coefficient between the dependent variables and a linear transformation of the explanatory variables.

利用伴随信息区分两个复合假设的大样本序贯检验AI 解读

The problem studied is that of utilizing measured concomitant information in sequential trials for the comparison of two treatments. The analysis is based on the treatment 1 minus treatment 2 response difference y = y 1 — y 2 and the corresponding concomitant observation difference x = x 1 — x 2, where x and y are assumed to be distributed bivariate normally. A simple asymptotically valid test procedure and its performance in Monte Carlo experiments are described. It is…

不同 k 类估计量对设定误差的相对敏感性AI 解读

The behavior of the probability limits of different k-class estimators under specification error is examined. Despite the fact that the probability limits are different when errors are not zero, it is shown that there exists no case in which either of the two leading estimators is uniformly more robust than the other if the criterion is any positive semi-definite quadratic form in the inconsistencies.

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利用回归技术生成全国月度零售估计的地区分解AI 解读

A common problem in sample estimation is the one of producing estimates for parts of the original universe (these parts are variously referred to in the literature as domains, subuniverses or subpopulations and may be defined in terms of areas or other characteristics). A technique is presented for producing these part-estimates when ratio or regression estimates are involved. This technique is used to produce estimates of retail trade for areas such as States, geographic…