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引入折扣权重的估计方法AI 解读

Summary In the estimation of the parameters in time series models arising in economic and business situations, it is often of value to introduce some method of discounting which produces updated estimators that give more weight to recent data than to that arising in the distant past. The simplest methods of introducing such discounting are to modify the traditional methods of estimation. Such modifications are discussed for the methods of moments, least squares and maximum…

Summary An unconditional non-parametric test for the bivariate two-sample problem is proposed. The test is shown to possess various desirable properties. We give critical values of the distribution, some approximations and its asymptotic distribution. For the shift type of alternative hypotheses, we show here that U is distributed asymptotically as a non-central chi-square. We have derived its Pitman's asymptotic efficiency relative to Hotelling's T 2 for these alternatives…

预先显著性检验后基于一个或两个样本的总体相关系数推断AI 解读

Summary It is shown in this paper that under certain restrictions on population parameters, estimates formulated on the basis of a preliminary test of significance concerning inferences for a population correlation coefficient are better than the usual unbiased estimators.

回归分析中的第二类模型AI 解读

Summary Regression models of the first and second kind are distinguished by the absence or presence, respectively, of variable regression coefficients. A characteristic of a model of the second kind is its heteroscedasticity. The problems of estimation in a general regression model of the second kind are discussed briefly. A more detailed examination is given of the properties of various estimators of the coefficients in the overall regression and scedastic curves for the…

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从削波平稳时间序列估计协方差与谱密度函数AI 解读

Summary When estimating the covariance functions of a stationary time series from a digitalized record, adjustments to the estimates must be made to correct for the bias caused by digitalizing. In this paper we investigate a method which provides consistent estimates of the covariance and the spectral density functions, and discuss their asymptotic efficiencies.

贝叶斯单次抽样方案的渐近性质AI 解读

Summary The model to be considered is based on a differentiable prior distribution, a general loss function, an operating characteristic written as an Edgeworth expansion, and sampling costs expressible as a polynomial in the sample size. Asymptotic expressions for the Bayesian single-sampling plan are derived and it is shown how previously known results may be found as special cases of the present one. The efficiency of non-optimum plans is discussed.

正交自变量下多元回归显著性的事后判定AI 解读

Summary In multivariate regression, when the regressors are orthogonal, the estimates of the coefficients may be regarded, in the normal case, as an independent normal random sample with estimable variance. Significance is determined by the absolute magnitude of the highest member of the sample, after consideration of order statistics more generally in this context. The method is applied to time series data analysed by Fisher and Yates (1957): while these authors identified,…

经典更新理论自然推广的渐近结果AI 解读

Summary A generalization of the classical renewal theory for non-negative summands is suggested which involves the maxima of the partial sums instead of the partial sums themselves. It is shown that the generalization is a natural one and that most of the classical properties are preserved. In addition, methods are developed for obtaining asymptotic expansions for the moments of the random variable whose expectation is the new renewal function.

回归参数与均值向量的固定宽度置信界AI 解读

Summary In this paper Chow and Robbins's (1965) sequential theory has been extended to construct a confidence region with prescribed maximum width and prescribed coverage probability for (i) the linear regression parameters, and (ii) the mean vector of a multivariate population. Except for the finiteness of the unknown variance and covariances in the respective two cases, no assumption regarding the form of their distribution functions is made. This result was announced in…

在拟合优度问题中使用未来观测的概念AI 解读

Summary An attack on the problem of goodness of fit is made by combining a Bayesian and sampling argument; the Bayesian part is effected by using the distribution of a future observation, while the sampling argument concerns itself with the distribution of a “chi-squared like” statistic, which measures discrepancies of observed frequencies from those predicted by the distribution of the future observation. Examples are given for the case of sampling from the binomial,…

将样本量视为随机变量时的假设检验AI 解读

Summary In the Neyman-Pearson theory of hypothesis testing it is customary to calculate significance levels and power functions on the assumption that the sample size is fixed. The main purpose of this paper is to propagate the view that the restriction of the theory to reference sets in which the sample size is constant is neither necessary nor desirable. The paper falls into two parts. In the first we consider the test of a simple null hypothesis versus a simple…

最小二乘拟合线性关系的若干研究主题AI 解读

Summary Various topics are reviewed: the effect of modern computers on statistical calculation; analysis by vector components rather than analysis merely of variance; “stepwise regression”; testing goodness of fit by examining residuals. Possible alternatives to the method of least squares appropriate when the distribution of errors has long tails, and computation of the likelihood function resulting from a Pearson Type VII distribution of errors, are considered. Some of the…

Summary A correction is made to a paper by Good (1963) on the independence of quadratic forms.

样本相关系数分布的若干新结果AI 解读

Summary A simple approximate normalization for the correlation coefficient in normal samples is obtained which is shown to compare favourably with previous normalization approximations (the usual large-sample normalization, Fisher's hyperbolic tangent transformation and Hotelling's improvement of that transformation). A second approximation, based on F and valid for large n | ρ | (n = sample size, ρ = population correlation), is also obtained. The results follow from a…

分位数估计的若干问题AI 解读

Summary The problem of estimating quantiles in the context where restriction to particular parametric families is inappropriate is considered, for simple random sampling and stratified sampling. For the former type of sampling the distribution-free procedures are obtained and the admissible estimators identified, and certain other questions are dealt with. In the stratified sampling situation similar problems are considered, less successfully.

分析稳定系统首达时间分布的一种方法AI 解读

Summary For many processes arising in reliability and congestion studies, passage time distributions required are difficult to exhibit. An asymptotic discussion is often available centring about a limit theorem given previously, and asymptotic equality of the mean passage time and an associated mean sojourn time, the latter obtainable directly from the ergodic distribution for the process. Theorems are presented exhibiting this equality for a variety of Markov chains.

可维修并联系统的可靠性AI 解读

Summary This paper derives expressions for the life-time distributions of systems consisting of a number of components in parallel, where repairs to these components are possible. These distributions reduce to those of first-passage times in a birth-death process or in a semi-Markov (or Markov renewal) process, and have application outside reliability theory. In the reliability context, the effects of altering the number of components and of increasing the repair facilities…

泊松输入下近满水坝模型的进一步结果AI 解读

Summary The dam model investigated has infinite depth, unit release per unit time, and inputs which form a compound Poisson process. The time-dependent content distribution for arbitrary initial content is obtained explicitly by a direct method and its asymptotic properties are investigated. The distribution of the time to first overflow as well as the probability of no overflow are also obtained explicitly by a similar method.

排序与滑移问题的若干渐近有效序贯程序AI 解读

Summary In this paper Chow and Robbins's (1965) sequential theory has been applied to ranking and slippage problems (including a multivariate slippage problem) and a class of asymptotically efficient sequential procedures is given for each problem. Except for the finiteness of the variance, no assumption regarding the form of the distribution function is made.

多元正态与 t 分布下凸多面体概率的计算AI 解读

Summary It is noted that probabilities of convex polyhedra in p-dimensional space can be expressed in terms of a function V(h1, h2, …, hp), if the distribution is normal, and in terms of a function Vn(h1, h2, …, hp), if the distribution is the t-distribution with n degrees of freedom. Formulae expressing V(h1, h2, …, hp) and Vn(h1, h2, …, hp) in terms of similar functions of lower order are obtained. An asymptotic expansion of Vn(h1,…, hp) in powers of n-1 is also included.…

具有泊松输入的近满水库模型AI 解读

Summary In this paper, the content of a dam with infinite depth, unit release per unit time and inputs which form a compound Poisson process is investigated by means of an integral equation technique. The Laplace transform of the content distribution for an initially full dam is calculated and inverted. The asymptotic behaviour of the content is described and its mean and variance obtained. Duality relationships with the almost empty dam with Poisson input are pointed out…

有限总体抽样的新方法（二）：分布无关充分性AI 解读

Summary The idea that in some situations the prior knowledge about the unknown parameters could be formulated as a class of prior distributions, which could be used, not necessarily through Bayes posterior probability, for subsequent inference, is already present in Godambe (1955). In the present paper, the concept of distribution-free linear sufficiency or in short linear sufficiency, originally due to Barnard (1963b) but redefined by the present author (Part I), is…