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参数估计中直接论证与信任论证的比较AI 解读

SUMMARY An approach to the problem of fiducial inference for dispersion on a sphere alternative to that adopted by R. A. Fisher is proposed.

拟合优度检验AI 解读

SUMMARY An explicit account is given of a procedure for assessing goodness of fit of some observations with a hypothesis, generally known as a “test of significance”; the description is close in spirit to R. A. Fisher’s original conception. The relation of this test procedure with Bayesian procedures and with the Neyman–Pearson theory of tests is discussed. Some very tentative suggestions are made regarding the choice of a test criterion and the use to which the result of…

二元反应曲线的序贯估计AI 解读

SUMMARY We suppose that it is required to estimate percentage points of a quantal response curve, and efficient use of observations is important. Strategies currently available are critically examined, including the Robbins-Monro process and Dixon and Mood’s Up and Down method. Some new alternative strategies are suggested and studied using empirical sampling on an electronic computer. The procedure recommended for estimation of 50 per cent. points has advantages of ease of…

三维列联表中的最大似然估计AI 解读

SUMMARY Interactions in three-way and many-way contingency tables are defined as certain linear combinations of the logarithms of the expected frequencies. Maximum-likelihood estimation is discussed for many-way tables and the solutions given for three-way tables in the cases of greatest interest.

用广义多项分布估计离散数据的相关性AI 解读

SUMMARY This paper presents a joint distribution for n identically distributed multinomial variates, Xq. The distribution is constructed so that C(Xq, Xr) = pV(X) for all q and r, q≠r, and applications of this model to the estimation of correlation in discrete data are discussed.

混合谱平稳过程分析（二）AI 解读

SUMMARY We investigate the asymptotic power functions of three types of tests for detecting the presence of harmonic components superimposed on a nonuniform spectral density function. These power functions are tabulated for a range of values of the signal to noise ratio of the process, and each test is applied to several artificial series of the “mixed ”type with known structure.

线性自回归模型拟合优度检验的抽样性质AI 解读

SUMMARY Sampling properties of tests for trend-free linear autoregressive schemes due to Bartlett and Diananda, to Quenouille, and to Whittle have been investigated. The investigation consists of the calculation of the first two moments of the various test-criteria which are χ2‘s with k degrees of freedom, where k is the number of asymptotically independent linear compounds on which the χ2‘s are based. The purpose is to examine the effect of the combination of individual…

一种简单的随机排列程序AI 解读

SUMMARY The paper describes a randomization procedure consisting in distributing a deck of cards into 10 decks using random decimal digits and repeating this step with each deck consisting of three or more cards. One random digit is used for randomizing a deck of two cards. This procedure, which is essentially a particular case of a general procedure described by Rao (1961), is called the multistage randomization procedure, or MRP. Some applications are described. A…

相对风险的近似置信限AI 解读

SUMMARY The relative risk or odds ratio has been proposed as one alternative to the difference in proportions in measuring the degree of association in two by two tables. This paper proposes two new methods for finding confidence limits on the relative risk, one appropriate for large numbers, and a second for small numbers. The first is related to the usual chi-square test and the second to an approximation to the Fisher-Irwin test. The methods are compared to those…

利用电子计算机分析非正交实验的均值与标准误估计AI 解读

SUMMARY Various methods of estimating means and standard errors for non-orthogonal designs are considered from the point of view of their generality and suitability for programming on an electronic computer. The use of the variance-covariance matrix is shown to have a number of advantages, and this method is described for designs with two or three classifications; the method of analysis for three classifications, no two of which are orthogonal, is new. Programmes have been…

论信推方法的一致性AI 解读

SUMMARY Lindley (1958) and Sprott (1960) have proposed several criteria for the satisfactory application of the fiducial method of inference to statistical problems. The criteria are concerned with consistency when there are various ways of applying the method. In sections 1 and 2 these criteria are discussed briefly, and the range of problems that yield fulfilment of the criteria is shown to be considerably larger than that indicated by Lindley and Sprott. A frequency…

多元正态分布均值的置信集AI 解读

SUMMARY An attempt is made to determine confidence sets for the mean of a multivariate normal distribution with known covariance matrix that take advantage of the fact that the sample mean is not the best estimate when the loss is a non-singular quadratic function of the error vector. Only the case of high dimension is considered. The geometrical size and shape of the confidence sets, the probability of covering false values, and the relation to posterior probabilities are…

多因素列联表中的交互作用AI 解读

SUMMARY Interactions in contingency tables are compared with interactions in the analysis of variance. The comparison leads to a new formulation of the hypothesis of no second-order interaction in three-way contingency tables, to an explanation of the paradoxes associated with this hypothesis and to a comparatively simple method of constructing its likelihood-ratio test statistic. The extensions to higher-order interactions are merely outlined as they are not likely to be of…

混合谱平稳过程的分析（一）AI 解读

SUMMARY We consider a normal stationary process whose spectrum may contain harmonic components superimposed on a non-uniform continuous spectral density function. The problem of separating the discrete and continuous spectral components is discussed, and it is shown that the bandwidth of the spectral density function must be restricted, in relation to the number of observations, in order to make the problem tractable. Assuming only that this bandwidth is known, the presence…

SUMMARY In this paper an investigation has been made of the problem of constructing systematic and randomized designs for the estimation of slope when the errors are autocorrelated. Some results are obtained for general stationary processes and specific designs given for moving average and autoregressive processes. Comparison is made with randomized block designs. The theory is illustrated on a time-series obtained from a uniformity trial on a batch production process.

谱密度估计AI 解读

SUMMARY A method of estimating spectral densities is developed which uses the data explicitly to help determine the best smoothing procedure. Two techniques are discussed. The first involves polynomial approximations, the second is an interpolation technique which is useful when a limited number of autocorrelations is available. The Gaussian and Laplacian weight functions play important roles in the first and second technique respectively.

总体算术均值乘积的估计量AI 解读

SUMMARY Symmetric functions which provide unbiased estimators for the product of m population arithmetic means are considered for two sampling procedures: (a) m independently selected simple random samples, and (b) a simple random sample of multivariate observations. Formulae for the variances of these estimators and for estimated variances are derived.

正态概率积分与 Mills 比率的新渐近展开AI 解读

SUMMARY Mill’s ratio can be expressed, for positive values of the argument x, as the Laplace transform, with argument x, of the function e−12t2. This enables a new, and superior, asymptotic expansion for Mill’s ratio to be obtained with the aid of a recent result on the asymptotic expansions of a wide class of Laplace transforms. The new expansion is considerably more accurate than the usual expansion.

某些次序统计量的渐近充分性AI 解读

SUMMARY The problem of estimating distance to a stellar system, from measurements on the apparent magnitude of the jth brightest object in the system, reduces to estimating the location parameter of a distribution. Astronomical observations provide apparent magnitudes of only a few of the brightest objects in a system. In this connection, two theoretical problems arise. One is to find the best estimate based on available observations, and the other to determine which of the…

矩阵广义逆及其在数理统计问题中的应用札记AI 解读

SUMMARY Some years ago the author defined a pseudo inverse of a singular matrix and used it in representing a solution of normal equations and for obtaining variances and covariances of estimates in the theory of least squares (Rao, 1955). This provided a unified approach to least squares theory, including the case when the normal equations become singular. This note attempts to collect a few mathematical results, some of which are known in literature, associated with the…

正态变量中若干二次型的分布AI 解读

SUMMARY This paper is concerned with the characterization of the variance covariance matrix for a normal family in which certain quadratic forms are independent and follow cχ 2 distributions. It is also proved that the necessary and sufficient condition for any quadratic or linear form to be distributed independently of a sum of a finite number of non-negative definite quadratic forms is that it is distributed independently of each one of them.

非正态性对方差分量估计的影响AI 解读

SUMMARY The effect of non-normality in estimating variance components in a random effects or mixed effects linear model is studied. It is shown that for a wide variety of balanced situations the interval estimation of the upper variance component is likely to be relatively little affected by non-normality in the error component. A method is suggested for constructing a confidence interval for a ratio of variance components in a balanced model, without assuming normality.

非线性估计中的精确信赖限AI 解读

SUMMARY In the problem of estimating an unknown parameter of a distribution (in normal regression or in more general situations), the determination of a point estimate and its distribution is contrasted with the setting of fiducial limits for the parameter value. The use of a point estimate is effective for setting fiducial limits only when the estimate is a sufficient statistic for the parameter. Exact fiducial limits can be determined for the non-linear parameters in a…

求解Leser最小二乘平滑方程的辅助序列AI 解读

SUMMARY Henderson’s method is applied to solve the equations which Leser uses for fitting a trend to a time series. In essence Henderson’s method depends on finding two quadratic factors for the symbolic expression 1+ϵ−1Δ4E−2. Two essentially different ways of factorizing this expression lead to two processes for fitting the trend, one of which is suitable when ε = 1 and the other when ϵ=13, 118 or 160. The methods are applied to an example considered by Leser for the cases…