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有限总体抽样的新方法：第一部分，充分性与线性估计AI 解读

Summary Barnard (1963) introduced the concept of linear sufficiency in connection with the Gauss-Markov set-up of estimation. In the present article the concept of linear sufficiency is redefined to suit the problem of estimation in survey sampling where, as demonstrated by the present author (Godambe, 1955, 1965), the Gauss-Markov set-up is fundamentally inapplicable. According to this redefined concept, a certain estimator is shown to be uniquely (up to a constant…

局部无偏的 M 型检验AI 解读

Summary In certain tests of hypotheses concerning more than one parameter, it is found that the criterion of unbiasedness cannot be satisfied. In such situations, it is proposed to make the test locally unbiased in a modified sense, termed Type M. Here the power surface in the parametric space does not always lie above the level of significance of the test. However, the mean value of the power, in a small neighbourhood of the null point, exceeds the significance level. This…

线性函数关系的广义最小二乘方法AI 解读

Summary A linear functional relationship between mathematical variables is postulated. The problem considered is the estimation of this relationship given observed random variate values, various assumptions being made about the distribution of the departures of these from the corresponding mathematical variable values. The least-squares principle is generalized to deal with cases in which these departures are correlated. The bivariate case is considered in detail. Extension…

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多元时间序列的指数平滑AI 解读

Summary A method is presented for estimating the optimum weight matrix for the exponential smoothing and prediction of multivariate time series. A recursive version of the estimation equations is given. A variation allows the estimation to forget the remote past in order to follow a process in which the structure varies slowly with time. It is pointed out that the method generalizes to non-linear processes when the non-linear structure is known. The practicality of the…

非平稳过程谱估计的设计关系AI 解读

Summary Further developments in the theory of evolutionary spectra are discussed, and some asymptotic results are derived in the sampling theory of spectral estimates. Various forms of “design” criteria for spectral estimation are constructed in terms of resolvability conditions, and it is shown that by introducing the concepts of “frequency-domain” and “time-domain” bandwidths, estimates may be obtained which satisfy the required conditions.

分层调整后比例异质性的卡方检验AI 解读

Summary In testing differences between proportions or rates of occurrence of events in different categories, expected numbers may be calculated separately within certain strata and subsequently summed over strata. For the Poisson case an approximate X2-statistic is derived as a simple modification of the usual test statistic. Other approaches and situations are discussed more briefly.

Bennett 二元符号检验渐近效率的一则札记AI 解读

Summary Asymptotic power properties of Bennett's bivariate sign test are studied by computing its Pitman efficiency relative to Hotelling's T2 test corresponding to the translation family of alternatives. The behaviour of the Pitman efficiency in some important special cases is also discussed.

两个随机变量的渐近序贯试验设计AI 解读

Summary Given two independent random variables with densities f1 and f2, we test H1: f1 = f11, f2 = f12 versus H2: f1 = f21, f2 = f22, where the fij are known densities (i,j = 1,2). We study asymptotic Bayes sequential procedures as the cost of each observation approaches zero. An asymptotic expression for the Bayes risk is found, and necessary and sufficient conditions for a decision rule to be asymptotically Bayes are derived. We study a class of tests which we call tandem…

有限决策问题的序贯复合规则AI 解读

Summary Asymptotically optimal rules are obtained for the sequential compound decision problem, where the component problem involves a finite parameter space and a finite action space. It is shown that under some regularity conditions the rule, which at each stage is a Bayes rule with respect to an estimate of the empirical distribution of the previous parameters, is asymptotically optimal. In the general situation, a randomized version of this rule is asymptotically…

关于 Welch–Peers 置信匹配先验的说明AI 解读

Summary Welch and Peers have shown that it is possible to determine a prior distribution for a one-dimensional parameter by requiring that the associated one-sided Bayes intervals are asymptotically confidence intervals. It is shown in this note that their procedure does not apply if certain natural two-sided Bayes intervals are used.

随机变量的关联与 Radon–Nikodym 导数的离散程度AI 解读

S. M. Ali, S. D. Silvey; Association between Random Variables and the Dispersion of a Radon–Nikodym Derivative, Journal of the Royal Statistical Society Se

非平稳过程预测量的递推关系AI 解读

Summary It is shown that if a process {xt} is generated recursively by a relation of type ∑j=0pajtxt−j=∑k=0qbktϵt−k+λt, where ajt, bkt and λt, are time-dependent sequences and {ϵt} is a process of unautocorrelated variables, then in general the linear least-square predictor of xt+m based upon {xs; s≤t}, denoted vt, obeys a recursion of the type ∑k=0qβktξt−k=∑j=0τcjtxt−j+vt, where r = max(p – 1, q – m). A method is given for obtaining the coefficients βkt, cjt and vt, and…

可估函数与广义逆矩阵的补充结果AI 解读

Summary A method is derived for calculating the unbiased estimator of any estimable function of the parameters of a linear model. its variance and its covariance with the estimator of any other estimable function are also obtained. An expression is also given for the F-value required in testing a general linear hypothesis.

次序统计量间距AI 解读

Summary The distribution theory and possible constructions for spacings (differences) between successive order statistics of a sample of independent and identically distributed random variables are reviewed. The problem of finding the limiting distribution of a function of spacings is discussed and some general limit theorems for such are presented.

平稳点过程强度函数的估计AI 解读

Summary The intensity function of a stationary point process gives as a function of x the conditional probability, given an event at time t, of an event in the interval (t + x, t + x + Δx). A very nearly unbiased estimate of the grouped intensity function is constructed. its sampling properties are investigated when the data are generated by a Poisson process.

随机逼近在过程控制中的应用AI 解读

Summary The objective of process control may be to hold a response Y as close to some specified target Y0 as possible by adjusting an independent variable X. In the simplest cases, this objective may be met by choosing a suitable fixed value of X as quickly as possible after the process is started up or after an unusual disturbance occurs during operation. In more complicated cases, it may be advantageous to continue the adjustment of X during normal operation. Two…

序列相关系数的矩AI 解读

Summary For a discrete first-order auto-regressive scheme (with initial value zero) xt = αxt-1 + ϵt, expressions have been found for the first four moments of α̂=∑1nxtxt−1/∑1n−1xt2. The expressions are of two kinds : (i) series in ascending powers of α2, (ii) asymptotic series in descending powers of n. A table of values of μ1‱,σ(α̂),β1(α̂),β2(α̂) is included. For the special case α2 = 1 the dominant terms in the first four moments are stated.

正态总体的平面截断AI 解读

Summary This paper considers the truncation of normal distributions by means of planes. The moment-generating function for the truncated distribution is obtained, and it is shown that, by suitable transformations, the problem reduces to the case of rectangular truncation.

通过贝叶斯定理推导一类概率分布AI 解读

Summary Being in some respects expository in character, this paper uses Bayes's theorem to derive a k-variate discrete probability distribution which is fundamental inasmuch as it proliferates, under various sets of asymptotic conditions, to yield as its limiting forms an array of other k-variate distributions including the multinomial, independent Poisson, independent negative binomial, independent gamma, Dirichlet and multivariate normal. A systematic arrangement of these…

多元正态分布参数的贝叶斯估计AI 解读

Summary A significant omission from the work of Raiffa and Schlaifer (1961) relating to a multivariate normal distribution is consideration of the case when the dispersion matrix is completely unknown. This paper partially fills the gap by applying the methods of Raiffa and Schlaifer to the particular problems of estimating the mean μ, the dispersion matrix ∑, and the generalized variance | ∑ |, when either or both of μ and ∑ are unknown.

采用整群抽样的分析性调查设计AI 解读

Summary This paper concerns the designing of certain analytical surveys (utilizing cluster sampling). The general concepts and problems peculiar to this type of study are discussed. The question of the relevant population for inference purposes is treated, and this is reflected in the model considered. Illustrations are given to clarify the situations where this type of model may be applicable. In general, the objective in planning such a survey is to select the sample so…

似然比检验与置信域检验AI 解读

Summary A previous paper (Aitchison, 1964) proposed a method of confidence-region testing for multiple-hypothesis situations and developed the theory for linear univariate situations and for the asymptotic parametric case. The present paper shows that the results for these situations are in fact special cases of a basic relation between confidence-region tests and likelihood-ratio tests. This relation allows the easy extension of confidence-region testing to multivariate…

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