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随机模型假设检验中卡方检验与似然比检验的小样本功效比较AI 解读

When applying the Markov model, it is often assumed the transition matrix is stationary and of order one. This article considers the problem of applying the transformed likelihood ratio statistic and the contingency statistic to testing the assumptions of a particular order and of stationarity when the assumptions are not true. A Monte Carlo study of the small sample power of both these test statistics shows that if the true alpha level is kept equal for the two tests they…

美国石油炼制行业的经济—线性规划模型AI 解读

The linking of statistically estimated relationships with an engineering linear programming model offers important potentials for simulation and forecasting models of industries. This article describes such a model of the U.S. petroleum refining industry. Econometric techniques are used to specify product demands, prices, and some technical adjustments. A linear programming specification of the production function, assuming cost minimization, determines crude oil input…

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正态变量二次型分布的一类新界AI 解读

Except in special cases, the distribution of a quadratic form Q in the normal random vector y cannot be expressed in closed form. However, bounds on the cumulative distribution of Q have been obtained by many authors. This article derives a new class of such bounds by means of a certain mixture representation for the distribution of Q. It is shown how the results apply to the problem of finding the distribution of ratios of independent quadratic forms in normal variates.

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两阶段最小二乘估计量的偏误AI 解读

This article derives the bias of the two-stage least squares estimator to the order of T-2, T being the number of observations. It is found that when the degree of overidentification in the equation concerned is unity, the 2SLS bias is zero to this order of approximation.

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二项数据存在分类误差时剔除切点附近观测的影响AI 解读

This article deals with the biasing effects of errors of measurement on the estimation of a population proportion or on the degree of association between two dichotomous variables. Consider a dichotomy that is formed by making a cut on an ordered scale, where errors of classification occur with greatest frequency in the neighborhood of the cut. It is demonstrated through numerical investigation that it is advantageous, both in terms of bias and of mean square error, to…

线性回归中二次曲线异常值的模型AI 解读

A model to describe a linear regression where outliers follow a quadratic regression is introduced and the asymptotic and small sample properties of the maximum likelihood estimators studied. The investigation demonstrates that parameter estimation in models which describe outlier patterns can provide a useful analytic procedure.

利用第二个样本估计对称分布族的尺度参数AI 解读

In this article we consider two classes of estimators of the scale parameter of a family of symmetric distributions which combine the information from two samples obtained from members of this family with possibly different scale parameters. Of the two classes one is based on a preliminary test of the equality of the scale parameters while the other is arrived at by minimizing the mean square error. These classes of estimators are studied from the point of view of efficiency…

两阶段最小二乘估计量一次迭代的渐近性质AI 解读

In this article we obtain the asymptotic distribution of the first iterate of iterated two stage least squares; we demonstrate that this distribution is different from that of the usual two stage least squares estimator. Moreover, we show that the difference in the covariance matrices of their respective asymptotic distributions is, generally, neither positive nor negative semidefinite. In particular, we produce examples in which for some parametric configurations this…

不完整数据下两样本问题的贝叶斯分析AI 解读

Suppose a sample of n units from a population with failure time cdf F(x) is put on test and the ith unit is removed from testing at min (xi, τi) where xi is the failure time of this unit and τi is a fixed truncation time. Similarly, let a second sample of units from be tested for times . A Bayesian approach for testing the hypothesis against the alternative based on such samples is considered. The posterior probability that (where k and the t's are defined later) is obtained.

交叉分类的关联度量（四）：渐近方差的简化AI 解读

The asymptotic sampling theory discussed in our 1963 article [3] for measures of association presented in earlier articles [1, 2] turns on the derivation of asymptotic variances that may be complex and tedious in specific cases. In the present article, we simplify and unify these derivations by exploiting the expression of measures of association as ratios. Comments on the use of asymptotic variances, and on a trap in their calculation, are also given.

已知测量误差方差的回归模型中条件均值与方差的比较AI 解读

When both variables in a normal regression model are masked by measurement errors of known variances, it is possible to obtain inferences about the parameters relating to the regression of the true variables. For two-sample problems, this article proposes tests of hypotheses of equality of (1) the regression coefficients and of (2) the residual variances, assuming a joint normal distribution on the predictor and predicted variables.

宽平稳自回归序列观测均值的估计AI 解读

This study concerns the relative efficiency of the least-squares estimator of the mean of a covariance stationary sequence that has a constant mean and an autoregressive representation of order p. Our results augment those in [2]. The results in Section 1 include for any positive integer p the variance of the LSE, the BLUE in terms of autoregressive coefficients, the variance of the BLUE and the range of applications of Ylvisaker's theorem [7] regarding a lower bound on…

正态分布方差的改进置信区间AI 解读

In considering the problem of confidence estimation for the variance of a normal distribution, Tate and Klett [5] raise two questions. “Does the interval of shortest length based on (, S2) depend only on ” (S2 denotes the sum of squared deviations.) “Among those intervals based only on S2 is the interval of shortest length necessarily of the form ” The answer to the first question is no; to the second, yes. The results are given for the general linear hypothesis model of…

半样本重复方差估计的部分平衡设计AI 解读

Half sample replication has been used as a method for estimating variances in stratified sampling whereby two primary selections are drawn from each stratum. This article considers some procedures of improving the precision of the variance estimator computed from a partially balanced set of half samples. Both the theoretical and empirical findings suggest that the SAOA procedure is an effective method to employ, in particular with a “2-order partially balanced design.”

线性模型异方差方差参数可作 MINQU 估计的充要条件AI 解读

Let y = Xβ+e be a Gauss-Markoff linear model such that E(e) = 0 and D(e), the dispersion matrix of the error vector, is a diagonal matrix whose ith diagonal element is σ2 i, the variance of the ith observation yi. Rao has recently brought out two sets of sufficient conditions (on X) for the MINQU-estimability of all the heteroskedastic variances. In this note, we have derived a set of necessary and sufficient conditions for the same purpose.

截断参数分布中 MVU 与 ML 分布函数估计量的比较AI 解读

The ratio of integrated mean square errors for minimum variance unbiased and maximum likelihood estimating distribution functions is computed for truncation parameter distributions as a relative efficiency measure. A “closeness” relative efficiency is also computed for these estimators for the same class of distributions. The MVU estimator is found to be more efficient than the ML estimator for all sample sizes exceeding two in both cases.

排序总体均值的双侧置信区间AI 解读

Suppose given k(≥2) populations π1, ···, πk such that observations from population πi have density function f(x—θi), x∈R, where the location parameter θi is unknown (1 ≤ i ≤ k). Assume Ef ≡ ∫∞ -∞ xf(x)dx < ∞. Let the population means be denoted by μ1, ···, μk and their ranked values by μ[1] ≤ ··· ≤ μ[k]. Dudewicz [1] gave upper and lower confidence intervals for μ[i](1 ≤ i ≤ k). We use these to obtain a class of two-sided intervals. For μ[k] Lal Saxena and Tong [2]…

正随机变量的负阶矩AI 解读

We investigate the problem of finding the expected value of functions of a random variable X of the form f(X) = (X+A)−n where X+A>0 a.s. and n is a non-negative integer. The technique is to successively integrate the probability generating function and is suggested by the well-known result that successive differentiation leads to the positive moments. The technique is applied to the problem of finding E[1/(X+A)] for the binomial and Poisson distributions.

峰度及相关统计量的进一步分析AI 解读

We develop a scale invariant test for one member of the family given by the symmetric densities c exp [—|x|θ], θ>0 against another member. The statistic which arises in testing θ = 2 (normal) against θ = 4 is then modified to make it also location invariant; this modification results in the kurtosis K of the sample. Three other statistics are proposed for testing light-tailed distributions against heavy-tailed ones; in particular, the ratio V of one-half of the range and the…