日期精度：到日 2575 篇 · 到月 3 篇 · 到年 0 篇
自回归序列拟合的简化方法
Summary The set of k equations arising from the asymptotic least-squares estimation procedure for fitting the unknown parameters in kth-order autoregressive models is shown to degenerate into two subsets, each of m equations for the even case (k = 2m), or two subsets, one of m equations and one of (m + 1) equations for the odd case (k = 2m + 1).
一类秩检验的渐近相对效率
Summary A partial ordering is introduced in a class of rank tests according to the weight or emphasis they place on the middle ranks versus the extreme ones. This notion of order is shown to be related to van Zwet's partial ordering of symmetric densities according to the probability in their tails. Bounds on Pitman's asymptotic relative efficiency (a.r.e.) of several tests to the Wilcoxon test are established. Finally, a sharp lower bound for the asymptotic power of the…
似然方法在含大量参数模型中的应用
Summary Likelihood methods of dealing with some multiparameter problems are introduced and exemplified. Specifically, methods of eliminating nuisance parameters from the likelihood function so that inferences can be made about the parameters of interest are considered. In this regard integrated likelihoods, maximum relative likelihoods, conditional likelihoods, marginal likelihoods and second-order likelihoods are introduced and their uses illustrated in examples. Marginal…
分枝扩散过程分枝点的估计
Summary A solution to the problem of estimating the positions and times of the branch points of a Brownian-motion/Yule process, given the positions of all the particles at a particular time, is outlined. A likelihood approach is used, and it is shown that the solution involves maintaining a clear distinction between likelihood and conditional probability if difficulties over mathematical singularities are to be avoided. Several unsolved mathematical problems are encountered,…
Behrens–Fisher 问题的序贯对应形式
Summary Srivastava (1966) proposed a class of asymptotically efficient sequential procedures for an analogue of the Behrens–Fisher problem. Recently, Robbins et al. (1967) also proposed the same class of sequential procedures. The object of this note is to give the details of our proof for the asymptotic efficiency, assuming only the finiteness of the variances. The multivariate analogue of this problem has also been considered.
广义逆矩阵在多元方差分析中的应用
Summary The concept of a generalized inverse matrix is used to derive the likelihood ratio statistic for testing a general estimable hypothesis in the multivariable linear model. The results, which are analogous to those in Searle (1965), are illustrated by considering the one-way model and the two-way model with one observation per cell.
若干位置参数估计量的渐近相对效率
Summary If, by analogy with means and medians, one computes that value such that the sum of the absolute pth powers of the sample deviations about that point takes on its minimum, one obtains an estimate of the central value of a symmetric distribution. Such estimates, for p ≥ 1 and under reasonable conditions, are known to be asymptotically normal as the sample size becomes large, and here the asymptotic relative efficiency of any pair is obtained, both for the general case…
二元多样本非参数检验
Summary A non-parametric test for the bivariate c-sample problem is proposed. The test is an extension of a bivariate two-sample test given by Mardia (1967) and possesses various desirable properties. We derive the asymptotic distribution of this test and obtain the Pitman efficiency of the test relative to Wilks's criterion A for the translation types of alternatives. We give the critical values of the distribution and some approximations. The test is applied to a numerical…
多重共线性与估计不精确
Summary For the standard linear model containing several explanatory variables, the precision of estimation of linear parametric functions is analysed in terms of latent roots and vectors of X'X, where X is the matrix of values of explanatory variables. This analysis provides a practical method for detecting multicollinearity, and it is demonstrated that it is also useful in solving problems of optimum choice of new values of explanatory variables.
β 最优检验及其在实验综合评价中的应用
Summary A concept of optimality of a test, based on the speed with which its power function reaches a pre-assigned value, is introduced and conditions for a test to have this property are considered. The concept is applied to the weighted combination of independent normal test statistics; tests for the presence of effects and for the equality of effects are deduced.
关于序贯估计的一则札记
Summary Moran (1951) infers that for some stationary stochastic processes, problems of parameter estimation may be simplified by employing sequential estimation procedures. He considers for example, estimation of the birth rate in the (stationary) Furry–Yule process. The purpose of this note is to indicate that Moran's suggestion may be useful for non-stationary processes as well. In particular, we consider maximum likelihood estimation of the parameter of a non-homogeneous,…
三维列联表中的卡方分解与偏关联检测
Summary This paper presents a method of partitioning a χ2 statistic for the I × J × K contingency table (viz. the χ2 statistic that is based upon the likelihood-ratio criterion for testing the null hypothesis that the three variables pertaining to the three-way table are mutually independent) into additive components that can be used to test (1) the null hypothesis of zero three-factor interaction, (2) the null hypothesis that the partial association between two of the…
两种终端决策与多阶段抽样下贝叶斯决策规则的渐近性质（一）
Summary The model is based on a differentiable prior distribution, a linear loss function, an asymptotically normal sampling distribution and sampling costs proportional to the sample size. Asymptotic expressions are derived for sample sizes, acceptance and rejection criteria and the minimum regret by minimizing the average regret for a k-stage sampling and decision procedure. The results generalize previously known results for k = 1 and 2 and bridge the gap to sequential…
线性贝叶斯方法
Summary A method of linear prediction is proposed, which follows the Bayesian scheme in combining prior and present information, but which uses only the first two moments of the distribution of parameters and observations, rather than the complete probability model required of Bayesian techniques.
正态线性回归系数的线性组合
Summary In the literature the double linear compounds of the multivariate linear normal regression coefficients are tested by using Roy's maximum root test, see, for example, Khatri (1962) and Morrison (1967, p. 109, equation (13)). The test statistic is Student's t. The t statistic gives narrower confidence bounds than those given by Roy's maximum root statistic. Morrison uses Hotelling's T2 statistic for testing linear compounds of the mean vector. However, the exact test…
复合决策与经验贝叶斯
Summary The analysis of a sequence of decision problems of identical structure is considered, and the similarities and differences between the compound decision and empirical Bayes approaches explored. The paper includes a brief review of the literature and examines the criteria which have been used in comparing compound decision and empirical Bayes procedures with conventional methods. The performance of one of these procedures is examined in detail, and the previously…
线性传染效应的检验：逆抽样
Summary Let Tr (r = 0, 1, …) be independent, positive, exponentially distributed random variables with parameters λ + rΨ. It is shown that the uniformly most powerful unbiased test of the null hypothesis Ψ = 0 against alternatives Ψ > 0 rejects the former for small values of Z=(∑r=1nrTr)(∑r=0nTr)−1. The power function of the test is given and the test is shown to be consistent. Unbiasedness is shown for a wider class of alternatives. A sequential version of the test is…
估计线性函数关系问题的“最大似然解”
Summary The problem considered is that of estimating a functional relationship (assumed linear) between two unobservable mathematical quantities ξ and η from pairs of observations on these quantities when both sets of observations are subject to normal independent errors. The problem has attracted much interest over a long period and one reads repeatedly that the method of maximum likelihood yields unsatisfactory estimators in this case. In this note we show that in fact no…
总体均值后验期望的一则札记
Summary It is a well-known result, see for example Lindley (1965) and Raiffa and Schlaifer (1961), that if x̄ is the mean of a sample of independent observations distributed N(μ, σ2) where σ2 is known, and if μ has been assigned a normal prior distribution, N(m, v), then the posterior expectation of μ, given the sufficient statistic x̄, has the form {x̄(n/σ2) + m/v}/{(n/σ2)+1/v}, that is, has the intuitively appealing form of a weighted average of the prior mean and sample…
关于概率与分位数的推断
Summary It is intended to make inferences on the basis of a set of observations resulting from n replicates of an experiment, where each observation X has distribution F(x; θ), in order to provide information about a future performance of the same experiment, or a small number of such future performances. In such a situation the inference should concern the probability of an event occurring in the future experiment, rather than directly concern the parameter θ (a vector in…
针对双侧备择假设的序贯检验程序
Summary A new sequential test procedure is introduced and compared with an existing procedure for testing a null hypothesis against a two-sided alternative hypothesis.
混合物试验：多重格点设计的估计回归函数
Summary Lambrakis (1968) introduced the multiple-lattice design for experiments with mixtures as a generalization of the simplex-lattice design introduced by Scheffé (1958), and derived the estimating regression function of the double-lattice design. In this paper an expression due to Savage (see Kiefer, 1961, footnote 6), which generates orthogonal polynomials on the points of a simplex-lattice, is used to derive the estimated regression function of any multiple-lattice…
二乘二列联表的精确贝叶斯分析与 Fisher 精确显著性检验
Summary A relationship is derived between the posterior probability of negative association of rows and columns of a 2 × 2 contingency table and Fisher's “exact” probability, as given in existing tables for testing the hypothesis of no association of rows and columns. The result for the 2 × 2 table is generalized to provide the posterior probability that one discrete-valued random variable is stochastically larger than another.
信赖论证及其在调查抽样中的应用
Summary Sprott (1960) proposed certain restrictions on distributions a posteriori in terms of the likelihood function. Hacking (1965) put forward a criterion for irrelevance restricting the choice of the pivots in terms of the likelihoods. This paper presents an extended application of Hacking's criterion to accommodate ancillary statistics. This extension is utilized to obtain the fiducial distribution of the mean of a survey (finite) population based on the given random…