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存在误分类和双重抽样的分类数据对数线性模型AI 解读

Errors in the collection of categorical data lead to misclassification of observed counts. Several authors have proposed a double sampling scheme. This article develops a method for analysis of double sampling data. First, a log-linear model is selected for the misclassification matrix that relates the fallible to the correct data; then another log-linear model is built on the distribution of the correct classifications. Thus, the error structure can be utilized in inference…

Spearman 秩相关及相关系数的精确非中心分布AI 解读

This article presents a general construction principle for the non-central distribution of Spearman's r without the usual reference to the underlying distributions of the two continuous random variables. The only distribution used is the bivariate distribution on the rank pairs in an n × n table. The noncentral distribution is generated by the calculation of the unequal probabilities of (n!)2 bipermutations. This distribution is approximated also by a skew distribution…

双因素方差分析中列调整行效应与简单行均值假设的等价条件AI 解读

In an unbalanced, fixed-effects, two-way analysis of variance there are three distinct, frequently encountered hypotheses, each of which can be described as a hypothesis of “no row effects.” This article derives necessary and sufficient conditions on the cell sizes for the “rows adjusted for columns” hypothesis to be identical to the “simple row means” hypothesis. The results in this article, together with previous results, complete the characterizations in terms of cell…

复合假设下的 Neyman 光滑拟合优度检验AI 解读

A method is given for adjustment of the Neyman smooth goodness-of-fit test to allow for estimation of parameters in a composite hypothesis. With this method the limiting distribution under the hypothesis is chi-squared, in contrast to a method given by Barton for this problem. The basis of the method is a standard modification of the quadratic score statistic.

光滑拟合优度检验的效率AI 解读

The smooth goodness-of-fit test of Neyman (1937) was generalized to composite hypotheses by Javitz (1975) and Thomas and Pierce (1979). The test statistic is derived, as is its local asymptotic relative efficiency (LARE), which permits its comparison with other quadratic score statistic (QSS) tests, which include a Pearson-type χ2 test. For testing the negative exponential and normal distributions, the smooth test is seen to have greater LARE than the Pearson-type test and…

系数尺度不均衡的正态变量二次型渐近展开AI 解读

When the coefficients in a quadratic form in normal variables are not all similar in size, the usual methods for computing the distribution fail to work well. An asymptotic expansion is given for the upper tail probability of such a quadratic form in which a few of the coefficients are comparable in size and the rest are much smaller. The accuracy of the approximation based on the expansion is investigated numerically.

非加性模型的贝叶斯分析AI 解读

A Bayesian analysis of a model for two-group experimentation is given. This model assumes that responses in one group are systematically related to responses in the other group through a general linear function using both multiplicative and additive parameters.

单峰密度下由分组数据界定矩、基尼指数与洛伦兹曲线AI 解读

In this article we first show how to extend the method for bounding ∫ h(x)f(x)dx from data grouped in intervals in which h(x) is convex and f(x) is decreasing to the case in which f(x) is unimodal. We then show that the unimodal density functions that bound ∫ h(x)f(x)dx for any convex function h(x) also bound the Gini index and the Lorenz curve.

两因素嵌套方差分量模型中变异占比的置信区间AI 解读

In the two-factor nested variance component model with equal numbers in the cells given by y ijk = μ + A i + B ij + C ijk , three important functions of the variance components σA 2, σB 2, and σC 2 are the proportions of the total variation due to factors A, B, and C, which are given by σA 2/(σA 2 + σB 2 + σC 2), σB 2/(σA 2 + σB 2 + σC 2) and σC 2/(σA 2 + σB 2 + σC 2), respectively. There are no exact confidence intervals available for these proportions. In this article…

正态总体位置突变的似然比检验AI 解读

An alternative to the hypothesis that the sequence X 1 ···, X n are independent and identically distributed normal random variables, with mean μ and variance σ2, is that the location parameter μ shifts at some unknown instant. The null distributions of likelihood ratio test statistics are given by Hawkins (1977) for the two cases of known and unknown σ2. Unfortunately, the null distribution for unknown σ2 obtained in that article is incorrect. In this article the correct…

有限总体子域估计的预测方法AI 解读

The problem of estimating finite population characteristics within subdomains is considered. Synthetic estimation has proved to be an important method for deriving such statistics. In constructing the statistics, one combines auxiliary information and sample estimators of the original domain of study. In this article we consider the construction of subdomain statistics as a prediction problem. We establish a superpopulation probability model and derive optimal predictors.…

多元众数与等值轮廓的迭代估计方法AI 解读

An iterative procedure for estimating the mode and isopleths of a multivariate distribution is presented. The mode is estimated by selecting a point from the final set in a nested decreasing sequence of convex sets, each one of which is iteratively the smallest closed, convex subset containing a certain proportion of its predecessor's data points. An isopleth is estimated by the boundary of the convex subset corresponding to a fixed number of iterations (independent of n).…

近似贝叶斯预测分布与模型选择AI 解读

An observation is assumed to arise from one of k models that may depend on parameters. A prior distribution is specified by assigning probabilities to each of the models and by assigning probability densities to the parameters of each model. If an approximate prior distribution is used, the predictive distribution of a future observation will be approximate. Bounds on the error in the predictive distribution are derived from bounds on the error in the prior distribution. A…

对《样条与约束最小二乘》的评论AI 解读

The flexibility of the restricted least squares (RLS) method described by Buse and Lim (1977) for cubic spline regression models is used to consider other polynomial splines. Some of the conclusions of the analysis of a sample data set in the Buse and Lim article are criticized for failing to consider less restrictive models. The data are reanalyzed, the end result being a simpler quadratic spline regression model.

历史时间序列的Karhunen–Loève分析：牙买加种植园出生数据应用AI 解读

A comparison of two spectral analysis procedures is presented: the frequency domain (Fourier transform) model and the Karhunen-Loève time domain model. Both models are used in turn to analyze a plantation births series during the period 1880–1938. The principal components model can be adapted as the discrete analogue of the Karhunen-Loève stochastic integral equation in order to decompose a single time series into trend, cycle, and seasonality. The results indicate that the…

存在窝效应时用刀切法估计毒理学数据中的比例AI 解读

The jackknifing methodology is proposed as a way of estimating and comparing proportions of affected fetuses in animal experiments. The estimate is a weighted average of the proportions in individual litters and is almost fully efficient in several cases of interest. The associated standard error is asymptotically correct for a wide range of possible models. Jackknife-based tests are shown to be competitive with other methods currently used.