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协变量不受控制时协方差分析的结构回归方法AI 解读

Analysis of covariance, with a single covariable in a randomized block design, is reconsidered in terms of structural regression. In practice, the covariable is often times uncontrolled, both in the experiment and in repeated sampling, and may follow a linear model as does the variable of interest. If the covariable is unaffected by treatments, then the covariable model may contain a block effect through no treatment effect. When such a model is adequate, the treatment…

矩阵的分数次幂AI 解读

Statisticians occasionally need to compute a fractional power of a matrix. In certain practical cases a matrix A is given, and the statistician wants to compute the pth power of A, where p is a fractional or negative number; that is, a matrix R, such that R 1/p = A. He can often get a satisfactory approximation to Ap by using several leading terms of a power series. This procedure is similar to that of inverting certain matrices by power series.

数据分组导致的分布无关检验效率损失AI 解读

While distribution-free procedures are often appropriate when testing statistical hypotheses, they may become complicated or involve loss of power when the data are grouped. For rank tests the ties caused by grouping are generally broken either by using a randomization procedure or averaging the tied ranks. In this paper the power loss due to equi-spaced grouping (in terms of Pitman asymptotic relative efficiency) is investigated for some commonly used tests, for each method…

信息性停止规则与总体规模推断AI 解读

It is a consequence of the likelihood principle that identical likelihood functions imply identical inferences. If the rule by which sample size is determined—the stopping rule—is reflected in the likelihood function, as it should be, apparently identical likelihood functions (without allowance for stopping rule) may in fact be different. This can happen if the stopping rules are informative. If the stopping rule is informative, the analysis must take the rule into account,…

移位泊松分布：B 参数区域AI 解读

The two-parameter (λ, r) probability function which arises from a generalization, px =λpx -1/(x+r), of the recurrence relationship between successive probabilities of a Poisson process, has been termed the ‘Displaced Poisson Distribution’ and is considered here over the parameter space λ > 0, r ≤ 0. Properties of the distribution are examined and estimators, when r is known and unknown, are derived by the methods of moment(s) and first frequency and by maximum likelihood.…

混杂析因设计中一致更优的组合估计量AI 解读

Many confounded factorial arrangements have the property of obtaining the same precision for any component of a particular main effect or interaction. A procedure for recovery of inter-block information developed by the author (Ann. Math. Statist 1964) is applied to such designs to obtain combined estimators having smaller variance than the corresponding intra-block estimators for all values of the inter and intrablock variances. The procedure has been illustrated for a…

正规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.

带协变量的指数生存分析AI 解读

In applied problems one often wishes to compare the mortality experience of two or more groups of individuals who are known not to be comparable with respect to a covariable. This paper presents an approach to this problem by assuming that the force of mortality for each individual is a function of the covariable. Extension to the case where more than one covariable is present is indicated. It is also suggested that the present method is adaptable to an actuarial type…

平稳随机过程中的离散抽样与移动和AI 解读

Assume that an autoregression generates the basic data but that the observations are an equi-spaced sample of moving sums of the basic data for non-overlapping discrete intervals. Simple least squares estimates of the underlying autoregression are not consistent. It is shown that it is possible to estimate consistently the coefficients of the underlying autoregression based on the equi-spaced sample. These results are equivalent to showing how to interpolate a finite number…

如何判断一种疾病是否具有家族聚集性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…

简单线性模型的线段置信带AI 解读

In this paper confidence bands are given for the entire line for simple linear regressions. The conventional bands that have been given in the past are curvilinear. In this paper we consider confidence bands that are straight lines. It is shown that under certain conditions the “width” of these straight line bands is less than the width of the conventional curvilinear bands.

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

种群与群落生态学中的多元对数级数分布及其统计性质AI 解读

A growing interest has been witnessed in recent years in multivariate discrete probability models. The multivariate logarithmic series distribution (LSD) is a multivariate analogue of the univariate LSD. This paper investigates the marginal and the conditional distributions of the multivariate LSD. It records its moment properties and also provides some regression and correlation analysis. An interesting modal property of the distribution is discovered. The paper also…

基于部分观测的样本均值与协方差多元预测区间AI 解读

By using the information provided by the first κ, 2 ≤ κ < N, members of a random sample of size N from a univariate normal distribution, Hickman [3] obtains prediction intervals for the sample mean, and the sample variance of the complete sample of size N. He gives similar results for a univariate normal regression model. Here we present straightforward generalizations of Hickman's results to the multivariate case.

多元正态分布均值的矩形置信域AI 解读

For rectangular confidence regions for the mean values of multivariate normal distributions the following conjecture of 0. J. Dunn [3], [4] is proved: Such a confidence region constructed for the case of independent coordinates is, at the same time, a conservative confidence region for any case of dependent coordinates. This result is based on an inequality for the probabilities of rectangles in normal distributions, which permits one to factor out the probability for any…

矩阵导数在多元分析中的若干应用AI 解读

It is claimed that the reasons for using matrices of derivatives, in appropriate situations, are as compelling as those for using matrices. This paper provides basic material for such use. Different types of matrix derivatives are defined and illustrated. Simple and easy techniques are then derived and are shown to be applicable to a considerable collection of matrix functions. Applications are made to such problems as establishing matrix integrals from scalar ones,…

二元极值分布的若干解析性质AI 解读

This article considers two examples of bivariate extremal distributions when the margins follow the first asymptotic distribution of the largest values. The variables are assumed to be reduced and each distribution contains only one parameter indicating the association between the extremes. The probability and the density functions of these distributions at the characteristic value, median, and mode have been analyzed. A procedure has been developed to estimate the single…

扰动同时存在序列相关与同期相关时回归方程组的有效估计AI 解读

This paper considers the problem of obtaining efficient estimates for the parameters of a system of M regression equations. The disturbance terms of this system are assumed to be related by both serial and contemporaneous correlation. Under the further assumption that the serial correlation is a first order autoregressive process, the paper develops an estimator that is consistent and has the same asymptotic normal distribution as the Aitken estimator which assumes the…

数据修订与经济预测AI 解读

The paper determines whether the earliest published indication of changes in GNP provide information which is useful in the interpretation of economic trends or whether subsequent revisions reveal that the true movements were radically different from those initially reported. An analysis of the provisional and advance data indicated that the initial changes differed from the final changes but still approximated the true pattern of the movements. Some of the data revisions,…

位置参数的稳健估计AI 解读

The problem of estimating a location parameter from a random sample when the form of distribution is unknown or there is contamination of the target distribution is attacked by deriving estimators which are efficient over a class of two or more forms (“pencils”) of continuous symmetric unimodal distributions. The pencils considered are the normal, double exponential, Cauchy, parabolic, triangular, and rectangular (a limiting case). The estimators considered are special…

摘要暂缺

混杂析因设计中一致更优的组合估计量AI 解读

Many confounded factorial arrangements have the property of obtaining the same precision for any component of a particular main effect or interaction. A procedure for recovery of inter-block information developed by the author (Ann. Math. Statist 1964) is applied to such designs to obtain combined estimators having smaller variance than the corresponding intra-block estimators for all values of the inter and intrablock variances. The procedure has been illustrated for a…

基于部分观测的样本均值与协方差多元预测区间AI 解读

By using the information provided by the first κ, 2 ≤ κ < N, members of a random sample of size N from a univariate normal distribution, Hickman [3] obtains prediction intervals for the sample mean, and the sample variance of the complete sample of size N. He gives similar results for a univariate normal regression model. Here we present straightforward generalizations of Hickman's results to the multivariate case.