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列联表交互作用检验：最小 Logit 卡方估计与最大似然估计的比较AI 解读

This article compares small sample properties of 12 goodness of fit tests for interaction in 2×2×2 and 3×2×2 contingency tables. The 12 tests are constructed by-combining three tests (the minimum logit chi-square test, the Pearson chi-square test, and the likelihood ratio test) and four methods of estimation (the iterative maximum likelihood estimator and three variants of the non-iterative minimum logit chi-square estimator). An evaluation is made of the adequacy of the…

包含初步显著性检验的假设检验AI 解读

Suppose that independent samples are available from two normal populations with means μ1 and μ2 and known variances. It is desired to test H: μ1 =0. A possible preliminary test procedure in this case consists of first testing μ1 = μ2 and then testing H using either the sample mean from the first population or the pooled sample mean depending on the outcome of the test regarding equality of μ1 and μ2. This procedure is shown to be biased. A power comparison of this procedure…

重复测量设计中均方比服从精确 F 分布的条件AI 解读

Investigation is made of the character of the covariance matrix which will result in exact F-distributions for the treatments and interaction variance ratios in repeated measurements designs. It is shown, assuming multivariate normality, that the matrix may exhibit a more general character than is typically implied to be essential. Equality of variances and equality of covariances, with identical matrices for all levels of a second treatment factor, are sufficient but not…

用于同方差检验的独立逐步残差AI 解读

Regression models which specify independent, homoscedastic and normally distributed errors may be analyzed in a stepwise manner to produce calculated residuals having this same property. If the nth residual is calculated as the deviation of the nth observation from its predicted value based on a least squares fit to only the first n observations then the resulting sequence of residuals, appropriately normalized, are not only mutually independent and homoscedastic but are…

响应曲面最小偏差估计的实验设计准则AI 解读

Minimum bias estimation for response surfaces is reviewed and the experimental design problem for this estimation procedure considered. A protection criterion is introduced and certain implications considered. The important single factor models are studied and results given. The criterion is also applied to a multifactor first order surface with protection against second and third order terms.

平稳时间序列的应用回归与方差分析AI 解读

In the area of applied time series analysis a commonly occurring problem involves the detection and estimation of signals (regression functions) imbedded within a collection of independent identically distributed noise processes. A general linear model which represents each observed time series as the sum of a wide sense stationary error process and a vector of regression functions operated on by a matrix of time invariant observables includes as special cases many signal…

ARIMA 时间序列模型中残差自相关的分布AI 解读

Many statistical models, and in particular autoregressive—moving average time series models, can be regarded as means of transforming the data to white noise, that is, to an uncorrected sequence of errors. If the parameters are known exactly, this random sequence can be computed directly from the observations; when this calculation is made with estimates substituted for the true parameter values, the resulting sequence is referred to as the “residuals,” which can be regarded…

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二元学生化最大模与最小模检验的功效AI 解读

Let t i = X i/s, i = 1, 2 be noncentral Student t-variates with noncentrality parameters δi, where x 1, x 2 and s are independent. The simultaneous distribution of t 1 and t 2 is studied and the power function of the studentized maximum and minimum modulus tests are tabulated for significance level 0.05, degrees of freedom 1, 2, 5, 10, 20, 50, ∞ and δ1, δ2 =0(1)5. Asymptotically exact approximations to these power functions are discussed. The marginal power of the maximum…

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纳入预先显著性检验的假设检验AI 解读

Suppose that independent samples are available from two normal populations with means μ1 and μ2 and known variances. It is desired to test H: μ1 =0. A possible preliminary test procedure in this case consists of first testing μ1 = μ2 and then testing H using either the sample mean from the first population or the pooled sample mean depending on the outcome of the test regarding equality of μ1 and μ2. This procedure is shown to be biased. A power comparison of this procedure…

综合急性医疗医院床位占用相关变量的随机模型AI 解读

A stochastic model for the behavior of the daily census in general-acute hospitals is presented. For any mix of elective and emergency patient day demand this model permits the computation of a complete set of measures of operating efficiency including expected overfill rate, percentage occupancy, waiting time for admission, waiting list length, and loss of emergency patients. This model extends previously developed models in important ways such as including the measurement…

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不等概率抽样中估计量及方差估计量的稳定性：样本量为3或4的经验研究AI 解读

Rao and Bayless [18] empirically investigated the stabilities of estimators of the population total and stabilities of their variance estimators for several methods of unequal probability sampling of two units (n =2) per stratum. In this article, after deriving the variances of variance estimators for general n for the following methods: (a) the I.P.P.S. (inclusion probabilities proportional to size) methods of Fellegi, Sampford and Carroll-Hartley, (b) Des Raj's and…

不完整列联表中的准独立性与最大似然估计AI 解读

Many authors have been concerned with contingency tables containing cells which are missing, a priori zero or otherwise specified. This article examines the problem of maximum likelihood estimation for such tables under the “quasi-in-dependence” model. In particular, conditions are provided to ensure the existence of unique nonzero maximum likelihood estimates for the cells of incomplete tables obtained by deleting the missing or a priori zero cells, even when other cells…

1954年与1963年大型都市区零售销售的决定因素AI 解读

This article presents several specifications of a retail sales model to explain the differential sales of retail goods and services in large Standard Metropolitan Statistical Areas in 1954 and 1963. Stepwise regression is employed and some hitherto unused regressors such as local government expenditures and taxes are introduced to compare different forms of the model specification. Tests on the stability of the relevant elasticities obtained in the model over time and on the…

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含误分类二项数据的双重抽样估计方案AI 解读

Two measuring devices are available to classify units into one of two mutually exclusive categories. The first device is an expensive procedure which classifies units correctly; the second device is a cheaper procedure which tends to misclassify units. To estimate p, the proportion of units which belong to one of the categories, a double sampling scheme is presented. At the first stage, a sample of N units is taken and the fallible classifications are obtained; at the second…

回归模型中普通最小二乘的效率条件AI 解读

For all regression models containing a common subset of explanatory variables, a necessary and sufficient condition for the ordinary least-squares estimators to be also best linear-unbiased estimators is given. The stochastic properties of the variances and covariances estimated by ordinary least-squares are derived. Five examples, especially useful in economic applications, are studied. The relevance of the basic result of this article for regression models containing a set…

二元两样本位置问题的 David–Fix 非参数检验AI 解读

Some large-sample properties of the three nonparametric tests of David and Fix for the two-sample bivariate location problem are given. In particular the Pitman A.R.E.s of the tests against some ‘normal-theory’ competitors are shown to be satisfactory in most cases for a number of ‘near-normal’ bivariate distributions. Their performances in some mixtures of bivariate normal distributions prove to be particularly convincing. A useful relationship between the three test…

析因实验交互作用的非参数估计与检验AI 解读

Some optimum nonparametric tests and estimates for contrasts of interactions in two-factor models with replications are proposed and discussed. These procedures are based on nonparametric estimates of the type considered by Hodges and Lehmann [4]. Unbiasedness and joint asymptotic normality of the estimates are proved and the asymptotic efficiencies relative to the least squares procedure is found. It is shown that, in the special cases of Wilcoxon and normal scores, these…

位置参数的渐近稳健估计量AI 解读

For the problem of efficiency-robust estimation of location, approximate versions are developed of optimally robust Pitman-type estimators. These are shown to have full asymptotic efficiency for a prototype family of distributions, used to define the estimators. The asymptotic efficiency under other distributions of interest is also characterized. For sample sizes n = 20, 30, 40, 50, and 100 the efficiencies were estimated by Monte Carlo methods under the following…

校准与统计推断AI 解读

This article presents an elementary statistical model from which inferences in the form of probability statements are drawn. These are compared with the inferences derived from the corresponding classical and Bayesian models of the same phenomenon. The example concerns a measuring device, and the problem of calibration is discussed. The method of analysis extends to a wide range of common statistical applications, notably those described by multivariate and linear regression…