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三参数对数正态分布的极大似然估计AI 解读

Summary Several authors (Hill, 1963; Box and Cox, 1964; Harter and Moore, 1966) have discussed the problem of estimating α, μ and σ2 where observations xi, i = 1, 2, ..., n, are available such that y = log (x + α) has a normal distribution with mean μ and variance σ2. In this paper it is shown that the difficulties encountered because the “likelihood” becomes unbounded are avoided if one takes into account the grouping error inherent in the data and uses the “correct”…

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微分方程参数估计中的混叠问题AI 解读

Summary This paper is concerned with the estimation of the parameters in a simple open-loop differential equation model. We suggest first some frequency-domain “narrow-band” and “broad-band” estimators that are based on the assumption that the observable input variable has no spectral mass beyond Nyquist frequency. We study the asymptotic biases of these estimators under the contradictory hypothesis that the spectral density of the input is a rational function of frequency.…

消除位置向量 Stein 型估计量的奇点AI 解读

Summary In estimating a multivariate location vector in three or more dimensions, it is well known that Stein-type estimators can offer considerable improvement in risk over the best invariant estimator. A common problem arising in the use of such estimators is that simple versions often have a singularity at zero. Methods of eliminating such singularities are discussed in this paper. The resulting estimators are usually considerably better than the uncorrected versions, and…

多元方差分析中的变量子集选择问题AI 解读

Summary As with most other multivariate techniques, methods such as discriminant analysis which depend on multivariate analysis of variance are affected adversely by the inclusion of irrelevant variables. This paper discusses the problem of finding a parsimonious subset of variables that is essentially as good as the full set. As a result of the close computational similarity to multiple regression, a stepwise procedure, and a best subset method are derived from their…

可信度推断AI 解读

Summary A scheme for inference—plausibility theory—is proposed. It parallels likelihood theory, the analogue of the likelihood function L(ω) = p(t; ω) being the plausibility function π(ω) = p(t; ω)/supt p(t; ω), but likelihood and plausibility throw light on different aspects of the evidence in the data t. The ordinate test for significance (which rejects for small values of the probability (density) function, of a simple hypothesis), the maximum ordinate estimate (which…

以次序统计量为节点的直方样条密度估计AI 解读

Summary The histospline considered here is a quadratic spline density estimate analogous to the Boneva–Kendall–Stefanov (BKS) histospline, with their equally spaced knots replaced by knots at every knth-order statistic. This estimate can be expected to be relatively more “flexible” where the density is greatest. We obtain “mean square error at a point” convergence rates. The rates obtained are uniform over classes of densities which have first (alternatively second or third)…

多元分析中的缺失值AI 解读

Summary This paper presents computational results for some alternative methods of analysing multivariate data with missing values. We recommend an algorithm due to Orchard and Woodbury (1972), which gives an estimator that is maximum likelihood when the data come from a multivariate normal population. We include a derivation of the estimator that does not assume a multivariate normal population, as an iterated form of Buck's (1960) method. We derive an approximate method of…

利用两个次序统计量估计 Weibull 分布参数AI 解读

Summary The use of a computationally simple statistic for estimating, from small samples, the important reciprocal-shape parameter, γ, of the Weibull distribution is described. The estimator uses two suitably selected order statistics from a sample of N failure times. The choice of the two has been made to minimize the variance of the estimator; however, concise formulae are given to permit the use of any two order statistics in the case of censored samples. The statistic is…

对称析因实验中的部分混杂AI 解读

Summary A new method is given for partial confounding with any block size in symmetrical factorial experiments. The method combines the techniques of confounding and incomplete block design, so that some factorial effects are completely confounded and some are partially confounded. A list of useful balanced incomplete block designs and group divisible designs is given, showing the wide range of available block sizes.

随机变量线性函数之比的分布渐近近似AI 解读

Summary Normal asymptotic approximations for the distribution of the ratio of linear functions of independent and identically distributed random variables are derived. These approximations are checked for accuracy by comparisons with exact known distributions in specific examples. In particular, the examples considered are the distribution of the circular serial correlation coefficient and Watson's distribution. The comparisons suggest that for sample sizes as small as 10 or…

二维列联表的贝叶斯估计方法AI 解读

Summary Estimation methods are proposed for the row, column and interaction effects in two-way contingency tables, the one-way table being treated as a special case. The methods are appropriate when the parameters are thought a priori to be related to each other. The posterior estimates have the practical effects of smoothing the contingency table, and are valid even if some of the cell frequencies are zero. The main case treated is where particular assumptions of…

随机离散分布AI 解读

Summary It is impossible to choose at random a probability distribution on a countably infinite set in a manner invariant under permutations of that set. However, approximations to such a choice can be made by considering exchangeable probability measures on the class of probability distributions over a finite set, and letting the size of that set increase without limit. Under suitable conditions the resulting probabilities, when arranged in descending order, have…

将 T 方法扩展至一般非平衡固定效应模型AI 解读

1. Introduction and Summary Among the various procedures for simultaneous interval estimation, Tukey's T-method gives the shortest confidence intervals for pairwise contrasts when it is applicable. (Cf. Scheffé, 1959, Ch. 3; Miller, 1966, Ch. 2.) However, the T-method in its exact formulation (excluding one way anova, see Spjøtvoll and Stoline, 1973) is restricted to well-balanced designs. In this paper we discuss a generalized T-type procedure for simultaneous interval…

Summary An empirical Bayes estimator which can be constructed without explicit estimation of the prior distribution is called a simple empirical Bayes estimator. Construction of such estimators for a single unknown parameter of a general continuous distribution is considered. Examples are given and their performance is examined.

参考值与估计方差对CUSUM检验平均运行长度的影响AI 解读

Summary An approximation, based on the Wiener process, is applied to Page's cusum statistic. Based on the average run length, the optimal reference value is determined analytically and shown to agree with results from studies using numerically determined run lengths. Next, we study the effect of using an estimate for variance and how this interacts with the choice of a reference value.

非中心参数置信区间的计算AI 解读

Summary The end points of a confidence interval for the noncentrality parameter of noncentral χ2 or F are identified as upper and lower percentage points of a distribution. It is shown how these can be calculated by applying the inverse Cornish–Fisher expansion. The same procedure can be used to find the value of the noncentrality needed to give a fixed size χ2 or F test some specified power; however, in this situation the results may be only approximate.

序贯概率比检验的错误概率与平均样本数AI 解读

Summary Let x 1, x 2, ... be independent random variables which under p θ have probability density function of the form exp (θx – Ψ(θ)} relative to some measure v, where Ψ is normalized so that Ψ(0) = Ψ‘(0) = 0. Let a ≤ 0 < b, sn = ∑1 n x k, and T=inf{n:sn∉(a,b)}. Approximations are given for p θ{sT ≥; b} and E θ(T) based on asymptotic considerations arising in renewal theory. The accuracy of these approximations is discussed for normally distributed x‘s. It is shown that…

线性后验期望的唯一性关系AI 解读

Summary When the posterior expectation of the population mean is a linear function of the sample observation, then the moments of the prior distribution are uniquely determined. From this, a fairly general condition is given for establishing that the prior distribution for the population mean has a unique form.

方向数据统计AI 解读

Summary Directional data analysis is emerging as an important area of statistics. Within the past two decades, various new techniques have appeared, mostly to meet the needs of scientific workers dealing with directional data. The paper first introduces the two basic models for the multi-dimensional case known as the von Mises–Fisher distribution and the Bingham distribution. Their sampling distribution theory depends heavily on the isotropic case and some developments are…

D 最优试验设计中的权重AI 解读

Summary We give a new proof of an inequality on design measures due to Attwood; the proof given here allows the investigation of when equality is attained. The result obtained is that, in a D-optimal design for a problem satisfying mild regularity conditions, either the number of distinct levels equals the number k of parameters and each level receives weight 1/k, or the number of levels is greater and each receives weight strictly less than 1/k. A complementary result…

整数受限参数空间中若干极大似然估计量的容许性与极小极大性AI 解读

Summary The present note studies the admissibility and minimaxity of maximum likelihood estimators in certain examples where the parameter space is restricted to integers.

存在干扰参数时的充分性与辅助性概念AI 解读

Summary Examples are presented to show how ambiguities may arise from attempts to define and apply analogues of sufficiency and ancillarity in the presence of nuisance parameters. It is necessary to tread with caution if one wishes to avoid inconsistencies or unexpected consequences inherent in principles which, on first acquaintance, appear unexceptionable.

Cramér–von Mises 统计量的分量（二）AI 解读

Summary Let θ^ be an asymptotically efficient estimator of parameter vector θ based on an ordered sample of n independent observations y 1, ..., y n from a distribution with distribution function F(y, θ) and let x^j=F(yj,θ^), j = 1, ..., n. Let Ŵn 2 be the Cramér–von Mises statistic calculated from ◯ 1, ..., ◯ n. This paper shows how to construct components ẑ n1, ẑ n2, ... such that Ŵ n 2 = ∑j=1 ∞ μj ẑ nj 2 where ẑ n1, ẑ n2, ... are asymptotically independent N(0, 1)…