日期精度：到日 2274 篇 · 到月 7743 篇 · 到年 0 篇
Fisher独立检验合并方法的渐近最优性（二）
It was shown by Littell and Folks [3] that Fisher's method of combining independent tests is asymptotically optimal among four commonly used methods of combining, according to Bahadur relative efficiency. The result of the present article is that Fisher's method is asymptotically optimal among essentially all methods of combining independent tests.
异方差线性模型的估计
This article considers the familiar linear model in which the residual vector e has elements e i with expectation 0 but different variances σ2 i . The elements of and the σ2 i are estimated by maximum likelihood under the assumption of a lower bound for the σ2 i of the form 0 < δ2 i ≤ σ2 i so that the likelihood is finite in the restricted parameter space. A second problem is considered in which the y vector splits into k sub-vector y j , such that all elements of y j have…
不完整数据下二元正态总体离散矩阵四种估计量的蒙特卡洛比较
Consider a random vector (X 1, X 2) distributed as a bivariate normal with mean vector zero, and dispersion matrix Σ = [(σ ij )]. Suppose we are given samples of sizes n 1 and n 2, respectively, from the marginals of X 1, X 2, and a sample of size n 3 from the bivariate population of (X 1, X 2). The problem is to obtain a good estimator of Σ based on this (incomplete) sample. In this article, four estimators of Σ are compared using Monte Carlo methods, and it is found that a…
聚类分析的概率理论
An explicit definition of a (k, r)-cluster is proposed. Each (k, r)-cluster has the property that each of its elements is within a distance r of at least k other elements of the same cluster and the entire set can be linked by a chain of links each less than or equal to r. Some exact distributional results are derived under a nonmetric hypothesis for the case k = 1. An example is given to illustrate the use of probability theory in identifying significant clustering…
连接点需要估计的分段多项式回归模型拟合
The study considers the problem of finding the least squares estimates for the unknown parameters of a regression model which consists of grafted polynomial submodels. The abscissae of the join points are a subset of the unknown parameters. Examples are given to illustrate how continuity and differentiability conditions on the model can be used to reparameterize the model so as to allow Modified Gauss-Newton fitting. A slightly generalized version of Hartley's theorem is…
评论：非参数位置参数推断的概率解释
The article by C.A. McGilchrist produces estimates and tests for certain location parameters in nonparametric contexts; numbers are attached to these estimates and tests, and probability interpretations are ascribed to the numbers. This commentary discusses the grounds for these probability interpretations. An example is given that shows how certain formal conditional-probability calculations can violate basic principles for conditional probability, and shows how the formal…
作者词汇量的估计
The problem of estimating an author's vocabulary, given a sample of the author's writings, is considered. It is assumed that the vocabulary is fixed and finite, and that the author writes a composition by successively drawing words from this collection, independently of the previous configuration. Attention is focussed on the random variable X(n), the total number of different words used in a sample of n. It is shown that under fairly general conditions, the distribution of…
不等错误率分配的Bonferroni检验扩展t与卡方表
Use of the Bonferroni inequality for controlling family Type I error rate is discussed and new tables of t and chi square are provided. The tabled percentage points provide the capability for unequal Type I error allocation over a family of statistical tests. Use of these tables is illustrated.
十种成对多重比较程序的蒙特卡洛评价
Computer simulation techniques were used to study the Type I and Type III error rates and the correct decision rates for ten pairwise multiple comparison procedures. Results indicated that Scheffé's test, Tukey's test, and the Student-Newman-Keuls test are less appropriate than either the least significant difference with the restriction that the analysis of variance F value be significant at α = .05, two Bayesian modifications of the least significant difference, or…
存在额外变异的比例数据：单样本与独立样本
Data which appear to be binomial proportions sometimes exhibit heterogeneity which results in greater variation than would be expected under the binomial distribution. Methods for estimating means and associated inference procedures in a single sample and one-way classification have been developed by a least squares approach in which estimates of the heterogeneity variances are obtained by moments and used in weighting. Monte Carlo studies of the performance of this…
纵向研究中的非参数方法
Inference procedures based on some simple rank statistics are proposed and studied for the statistical analysis of longitudinal data. These robust and asymptotically efficient procedures do not require the basic assumption of multivariate normality of the underlying distributions. The theory is illustrated with two examples.
一类协方差不等式
This article considers the class of covariance inequalities of the form cov (X,Y) ≤ var g(X,Y). We present a functional inequality and a partial differential inequality, each of which is a necessary and sufficient condition on g for the covariance inequality to be satisfied for all random variables X, Y jointly taking values in a given region.
多个 Bernoulli 参数函数的置信区间及可靠性应用
The estimation of functions of Bernoulli parameters is of interest in reliability theory. In this article, the theory of exponential families is used to obtain exact confidence limits for products and quotients of Bernoulli parameters when negative binomial observations are available from each population. Sampling methods based on compound Poisson distribution are suggested for estimating more general functions such as sums of products of Bernoulli parameters. Finally, it is…
离散概率函数线性组合的最大似然估计
In this article the problem of obtaining the maximum likelihood estimates of the parameters from a special type of linear combination of discrete probability functions is discussed. It is shown that when the sample is completely categorized the estimation problem is no more complicated that that of estimating the parameters of each of the component probability functions separately. When the sample is less than completely classified an iterative procedure must be used to…
Spearman–Kärber 与最大似然均值估计的等价性
In this article, we show that two methods of estimating the mean of a distribution using quantal response data are often equivalent. The two estimates considered are the Spearman-Kärber and an estimate discussed in a previous article by the authors [4]. The latter is based on a maximum likelihood solution for a nonparametric problem.
指数族中最大似然与加权最小二乘估计的等价性
In this article it is shown that weighted least squares estimators for the coefficients of a multiple regression model are the same as the maximum likelihood estimators when the dependent observations are from a member of the regular exponential class of distributions.
方差齐性的大样本稳健检验
Two asymptotically robust tests for equality of variances in the k-sample case are discussed: a simple X 2 test and a test based on the jack-knife procedure. Some Monte Carlo experiments suggest that these tests are reasonably robust for moderately small samples, are more powerful than Box's grouping test and perform similarly to Bartlett's test in the normal case.
最大复相关系数的选择：渐近情形
Selection of t largest from among k independent multiple correlation coefficients, , is provided by a procedure with the property that the probability of a correct selection is not smaller than a preassigned P* whenever the t largest θ i (1) exceed each remaining θ i by a magnitude δ1, and, simultaneously, (2) each θ i is at least δ2 times as large as each remaining θ i . The separation thresholds, 0 < δ1 < 1 and δ2 > 1 are also preassigned. Several applications are…
Stein 估计规则及其竞争方法：经验贝叶斯视角
Stein's estimator for k normal means is known to dominate the MLE if k ≥ 3. In this article we ask if Stein's estimator is any good in its own right. Our answer is yes: the positive part version of Stein's estimator is one member of a class of “good” rules that have Bayesian properties and also dominate the MLE. Other members of this class are also useful in various situations. Our approach is by means of empirical Bayes ideas. In the later sections we discuss rules for more…
回归中预检验估计量的统计后果
This study is concerned with deriving the properties of the preliminary test estimator for the general linear normal regression model, ascertaining the characteristics of the risk functions over the parameter space, and determining the conditions necessary for the risk of this estimator to exceed or be less than the conventional one under squared error loss. A test procedure and the problem of choosing an optimal level of significance for the test are discussed. Some…
多元回归变量选择的停止规则
Stepwise regression is a member of a class of statistical methods which may be called opportunistic. The statistician is naturally concerned that an artifact should not be reported so he needs a stopping rule that is geared to the way in which variables are selected. A sampled permutation test is outlined which offers such a stopping rule for forward stepping.
个人公司股票持有的应计资本利得估算
Stock market gains, their sources and economic effects have been the subjects of several recent studies, but the estimates of accrued gains generated in these studies often differ considerably, and do not meet some simple tests of consistency. In this article, an analytical framework is developed for computing capital gains consistently. The holdings of nonprofit institutions, which are generally not separated from the household sector because of lack of satisfactory data…