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极值理论中的超慢变函数AI 解读

Summary Large-deviation limit theorems for maxima of random samples in the domain of attraction of the extreme value distribution Φα are studied, motivated by examination of an approximation used in the statistical analysis of large observations. The large-deviation property is shown to be equivalent to a strengthened form of slow variation condition, called here super-slow variation, on the tail of the distribution of a single observation. Various conditions for super-slow…

矩阵的加性与乘性模型最小二乘逼近AI 解读

Summary Reduced rank approximation of matrices by Householder–Young methods is shown to be equivalent to fitting of a bilinear (multiplicative) model and to projection onto an optimally chosen subspace. The relation to linear approximation is made evident. Least squares fitting of a mixed linear (additive) and bilinear (multiplicative) model is proved to be a two-stage process: (1) fit the linear part of the model, then take residuals, and (2) fit the bilinear part to the…

关于潜根回归中乘子的一个注记AI 解读

Summary A recent treatment of multiple regression involves the use of Lagrange multipliers. These multipliers are explicitly characterized in this note as partial covariances.

多重指数平滑中的矩阵求逆札记AI 解读

Summary In discussing the equivalence of certain polynomial predictors, Godolphin and Harrison (1975) note a matrix U employed in Multiple Exponential Smoothing whose inverse has not been obtained explicitly. The inverse of a related matrix p is obtained here and the relationship between the two matrices U and p reveals why no inverse has been obtained in general for U.

空间点过程的参数估计AI 解读

Summary In a recent paper, Ripley (1977) discusses the use of two goodness-of-fit criteria for spatial point pattern data. Both criteria can be adapted to the associated problem of parameter estimation. to illustrate their use in this respect, we re-work one of Ripley's examples and reach rather different conclusions.

密度估计、随机过程与先验信息AI 解读

Summary A method is proposed for the non-parametric estimation of a probability density, based upon a finite number of observations and prior information about the smoothness of the density. A logistic density transform and a reproducing inner product from the first-order autoregressive stochastic process are employed to represent prior information that the derivative of the transform is unlikely to change radically within small intervals. The posterior estimate of the…

向量移动平均过程的精确与近似最大似然估计AI 解读

Summary This paper derives the exact likelihood function for the vector moving average process; the method used is a generalization of that adopted by Box and Jenkins (1970, Appendix A7.4) for the univariate process. Tunnicliffe Wilson (1973) has previously considered the estimation of parameters in multivariate time series models, and his procedure for moving averages is shown to be an approximation to maximum likelihood. A procedure for the computation of the exact…

光滑回归函数的非参数估计AI 解读

Summary This paper presents a new family of non-parametric estimators of a smooth regression function, which are shown to have theoretical advantages in small samples over some alternative estimators. The new estimator has practical computational advantages over spline functions, while its smoothing properties are very close to the optimal smoothing properties of cubic splines. A simulation experiment demonstrates the remarkable success of the cross-validation technique as a…

贝叶斯生命表分析AI 解读

Summary The moments of the posterior p.d.f. of the probability of surviving to time t, P(t), are obtained, assuming a time-dependent Poisson process for failures and i.i.d. gamma prior densities for the hazard function. For improper densities the results reduce to the Kaplan–Meier estimate of p(t) and to the Cox result for the comparison of two survival curves, which, because of the use of improper priors, may be inadmissible with respect to mean square error loss. A way of…

Lehmann 模型下多样本指数得分检验的性质AI 解读

Summary Properties of an exponential scores statistic which provides a non-parametric test of the homogeneity of k continuous populations are considered. Tables of exact critical values are given for the case k = 3 and some small sample sizes and approximations to the critical values are developed and evaluated. Small sample power comparisons are made with the Kruskal–Wallis rank test under the Lehmann model and some asymptotic efficiency results are developed under a…

高斯格点模型的变量测量误差估计AI 解读

Summary It can happen that the variates of primary interest in a simple Gaussian lattice scheme are not directly observable. An errors-in-variables formulation may then be appropriate. This note describes the corresponding maximum-likelihood estimation of unknown parameter values. An example is given.

Wiener–Kolmogorov 预测器的渐近性质（二）AI 解读

Summary The asymptotic properties of the autoregressive estimates a (T)(u) obtained using the fles method (Bhansali, 1974) suggest that, in practice, a decision on truncating the a (T)(u) at u = p, say, will need to be taken. This truncated sequence of the auto-regressive estimates is used to form alternative estimates of the linear predictor, the autoregressive spectral density function and the innovation variance. Some of the asymptotic properties of these estimates are…

不透明空间样本的抽样理论AI 解读

Summary Procedures for inferring the internal geometric structure of an opaque bounded n-dimensional set by random sectioning are discussed. General conditions are given (evidently for the first time) for the validity of the so-called “fundamental formulae” of stereology (the science of inferring spatial structure from lower dimensional data). In technical terms, a wide class of unbiased ratio estimators, based on the traces of embedded features in appropriately weighted…

平稳点过程中事件间隔的连续时间谱分析AI 解读

Summary The sequence of intervals between events in a stationary point process is considered as a process in continuous time. Expressions are given for a covariance function and the corresponding spectrum. Some examples are given to illustrate that the properties of the intervals as a process in continuous time are not the same as those of the intervals as a sequence. The methods developed are used to analyse a process consisting of times of R peaks in an electrocardiogram…

交叉验证与 Akaike 准则选择模型的渐近等价性AI 解读

Summary A logarithmic assessment of the performance of a predicting density is found to lead to asymptotic equivalence of choice of model by cross-validation and Akaike's criterion, when maximum likelihood estimation is used within each model.

方向统计中的 von Mises–Fisher 矩阵分布AI 解读

Summary When n distinguishable directions in p dimensions are required to describe each orientation, Downs (1972) has extended the von Mises–Fisher distribution. We obtain the normalizing constant which leads to the investigation of various basic properties of the distribution. In particular, an explicit expression for the first population moment as well as the asymptotic distribution of the basic statistics are provided. The estimation problem, important testing problems,…

通过 EM 算法对不完整数据进行最大似然估计AI 解读

Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least…

Professor A. M. Kshirsagar has pointed out that the un-numbered Lemma at the top of page 135 of Hawkins (1976) and the distributional result lower down in the page for the noncentral case are proved within the general context of canonical correlation in Kshirsagar (1972) pages 320 to 325.A special case is also to be found in Kshirsagar (1961).

保守统计推断AI 解读

Summary It is argued that statistical problems can usefully be divided into two classes: one-person problems for which Bayesian techniques are appropriate, and many-person problems, for which Bayesian techniques are not appropriate. Two conditions are presented which it is felt that statistical procedures for many-person problems should satisfy. Some of the consequences of these conditions are then investigated and discussed.

多元回归中的变量选择：同时检验程序的应用AI 解读

Summary Simultaneous procedures for variable selection in multiple linear regression have recently been given by Aitkin. One of these procedures, proposed for the case when the regression equation is to be used for descriptive purposes, is an application of each of a number of simultaneous procedures concerned with the multivariate general linear model and given by Gabriel with applications in the manova context. The applications of Gabriel's procedures to multivariate…

与皮尔逊矩比统计量相关的 Cramér–von Mises 型拟合优度统计量AI 解读

Summary We investigate a statistic introduced by de Wet and Venter to test for normality and a Cramér–von Mises statistic asymptotically equivalent to this statistic. It is shown that the Cramér–von Mises statistic can be written as a sum of components which are polynomial functions of the original standardized observations, the most important of which are Pearson's moment ratio statistics, √b 1 and b 2. Approximate small sample percentage points are given for the de Wet and…

具有超几何概率的一般离散分布族AI 解读

Summary A three-parameter family of distributions which belongs to Kemp's wide class, and which extends a two-parameter family of Katz, is investigated. Relations involving moments and probabilities are utilized in obtaining minimum χ2 estimators of the parameters. The asymptotic relative efficiency of various estimators is compared and a numerical example given.

回归分析若干相关问题的边际似然解法AI 解读

Summary In the linear regression model when the design matrix x is a function of a set of unknowns ρ, a marginal likelihood is derived for making inferences about p. Several special cases are considered and a numerical illustration is given.

通过最大值随机变量的分布识别参数AI 解读

Summary Under what conditions does the distribution of the maximum of a set of independent random variables uniquely determine the distributions of the component random variables? In the univariate case, a sufficient condition is that for every pair of distinct densities in the family of possible densities, one density converges to zero infinitely faster than the other, as x → ∞. Hence, the distribution of max {X i, i = 1, ..., n} when X i has the distribution N(μi, σ2 i),…