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正则或遍历转移矩阵的不动点概率向量AI 解读

A simple form for the fixed point probability row vector of regular or ergodic transition matrices is developed using some of the theory of generalized matrix inversion, together with the well known existence and uniqueness of a fixed point probability row vector. The forms for both the regular and ergodic case are identical and afford the easy calculation of the fixed point without calculating powers of the transition matrix or considering the usual convergence methods.

疾病是否具有家族聚集性的统计问题AI 解读

In trying to determine whether a disease is familial, epidemiologists often locate a source of cases and compare the proportion of affected relatives of these cases with that of the relatives of controls by the usual fourfold table techniques. In the model considered here, following Haenszel [5], the probability of being affected is a random variable, ρ, which is constant for members of the same “family” but which may vary from family to family. The usual tests are examined…

拟合优度AI 解读

This Paper defines a class of distribution free measures of goodness of fit; their exact distribution for small samples can be calculated by means of a computer. Two of them have the same asymptotic distribution as the Kolmogorov-Smirnov statistic.

摘要暂缺

指数与幂函数总体样本中若干统计量的分布AI 解读

The distributions of linear forms of m independent exponentially distributed random variables T 1, T 2, · · ·, Tm or linear forms of the variables T(1), T(2), · · ·, T( m ) (where T( i ) is ith order statistic) are considered. The results are used for the determination of the distributions of products of powers of the variables Z 1, Z 2, · · ·, Zm (or of order statistics Z(1), Z(2), · · ·, Z( m )) which have the power-function distributions.

对成对残留效应平衡的序列设计AI 解读

Finney and Outhwaite [2] introduced serially balanced sequences into the statistical literature. They classified these sequences into two types, viz., type I and type II. Sampford [3] gave many methods of construction and analysis of these sequences. But these authors were concerned only with sequences balanced for a single residual. We shall deal with sequences balanced for pairs of residual effects. Two important methods of construction of these sequences are given. One is…

离散情形下位置参数的 Wilcoxon 置信区间AI 解读

The paper surveys results about the behavior of nonparametric methods in cases where the customary continuity assumptions are not satisfied. A projection approach is used to show that true confidence coefficients associated with confidence intervals for appropriate location parameters derived from Wilcoxon one- and two-sample tests are at least equal to the nominal level for the continuous case, if the confidence intervals are considered closed, at most equal to the nominal…

回归分析中扰动估计的进一步讨论AI 解读

For the well-known general linear model Theil has recently developed the so-called best linear disturbance estimates with a covariance matrix equal to σ2 I. In this article we give a slightly different formulation of his problem which may give us some more insight in this estimation procedure. An important check on the computations of these estimates is given, as well as a comparison of these estimates with the commonly used least-squares estimates. For some special cases…

Zellner 似不相关回归方程估计量的无偏性AI 解读

The purpose of the present note is to demonstrate the unbiasedness of Zellner's seemingly unrelated regression equations estimators under fairly general conditions.

用于计量经济分析的数据季节调整AI 解读

An earlier paper [3] provides axioms for the seasonal adjustment of economic time series. Seasonally adjusted data should be minimum variance, unbiased, and linear in an appropriate sense. These axioms yield a unique method for seasonal adjustment. The seasonally adjusted data may be obtained by an application of ordinary least squares regression.1 The problem of seasonal adjustment of economic time series in [3] is not the same as the problem of seasonal adjustment of data…

多元分析中求解离散矩阵函数零点的算法AI 解读

This paper is devoted to a discussion of an iterative procedure for obtaining the maximum likelihood estimator of the covariance matrix for multivariate experiments in which measurements on certain components of a normal vector random variable are intentionally omitted in corresponding subgroups of the experimental units. The proposed algorithm, which is based on the Newton-Raphson method, is outlined in detail in Section 5. A special design is included to illustrate the…

存在无应答时的最优样本设计AI 解读

Discussed here are several aspects of a simple model for dealing with nonresponse. The model is, in a sense, a sequential one and is developed from a Bayesian decision theory point of view. Within this framework we examine how formalization and combination of one's opinions, past experience, and “objective” evidence concerning the proportion of non-respondents, the differences and relations between respondents and nonrespondents, the cost of obtaining information from…

多元统计中的缺失观测（二）：简单线性回归的点估计AI 解读

We define and evaluate some simple estimators of the linear regression function of y and x, when observations may be missing on y or x. In particular, we compare the zero order estimator, a modified zero order estimator, and mixed estimators relative to the least squares estimator using the ratio of expected mean square errors as our measure of efficiency. Illustrative tables are given to support our conclusions regarding the estimator of choice.

摘要暂缺

双重非中心 t 分布的矩AI 解读

This paper gives analytic expressions for the moments and recurrence relations for the first four raw moments of a doubly noncentral t-distribution with v degrees of freedom and noncentrality parameters δ and λ. Table I provides numerical values of these moments for v = 2 (1) 20, λ = 2 (2) 8 (4) 20 and any suitable δ. Two approximations to the t″-distribution, involving the moments, are considered.

二项试验中零失败概率的估计AI 解读

The maximum likelihood estimator and minimum variance unbiased estimator of the probability of zero failures in m binomial trials were compared on the basis of expected squared estimation error. The choice of estimator proved to be a function of the region of parameter space. However, the m. l. e. was preferred throughout the regions likely to be encountered in practice (where the probability of zero failures exceeded 0.5).

多元泊松分布中的回归：一则札记AI 解读

The regression of Xp on X 1, · · ·, Xp -1, when the random vector X = (X 1, · · ·, Xp ) follows a p-variate (p > 2) Poisson distribution, is obtained. Various sets of sufficient conditions for the linearity of the regression are given. It is shown that the regression is linear in one of the regressors if all the rest are zero, without any restrictions on the distribution of X.

关于 Fellegi 不放回规模比例抽样方法的札记AI 解读

In 1963 Fellegi proposed a new method of sampling without replacement with probability proportional to size, which allowed for rotation of the sample (within certain limits) simultaneously with the exact calculation of joint probabilities of selection of sets of units. Fellegi was able to show that for samples of size two units his equations always yielded a solution, provided that the largest of the population units did not exceed one third of the size of the whole…

一种多元指数分布AI 解读

A number of multivariate exponential distributions are known, but they have not been obtained by methods that shed light on their applicability. This paper presents some meaningful derivations of a multivariate exponential distribution that serves to indicate conditions under which the distribution is appropriate. Two of these derivations are based on “shock models,” and one is based on the requirement that residual life is independent of age. It is significant that the…

摘要暂缺

指数分布与幂函数分布样本中若干统计量的分布AI 解读

Abstract The distributions of linear forms of m independent exponentially distributed random variables T 1, T 2, · · ·, Tm or linear forms of the variables T(1), T(2), · · ·, T( m ) (where T( i ) is ith order statistic) are considered. The results are used for the determination of the distributions of products of powers of the variables Z 1, Z 2, · · ·, Zm (or of order statistics Z(1), Z(2), · · ·, Z( m )) which have the power-function distributions.

多元泊松分布中回归的一个注记AI 解读

The regression of Xp on X 1, · · ·, Xp -1, when the random vector X = (X 1, · · ·, Xp ) follows a p-variate (p > 2) Poisson distribution, is obtained. Various sets of sufficient conditions for the linearity of the regression are given. It is shown that the regression is linear in one of the regressors if all the rest are zero, without any restrictions on the distribution of X.

离散情形下位置参数的 Wilcoxon 置信区间AI 解读

The paper surveys results about the behavior of nonparametric methods in cases where the customary continuity assumptions are not satisfied. A projection approach is used to show that true confidence coefficients associated with confidence intervals for appropriate location parameters derived from Wilcoxon one- and two-sample tests are at least equal to the nominal level for the continuous case, if the confidence intervals are considered closed, at most equal to the nominal…

In 1963 Fellegi proposed a new method of sampling without replacement with probability proportional to size, which allowed for rotation of the sample (within certain limits) simultaneously with the exact calculation of joint probabilities of selection of sets of units. Fellegi was able to show that for samples of size two units his equations always yielded a solution, provided that the largest of the population units did not exceed one third of the size of the whole…