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贝叶斯模型监测AI 解读

SUMMARY A simple method of monitoring the predictive performance of a class of Bayesian models is introduced. The models involve sequential analyses of sequences of observations and are appropriate for a variety of monitoring and forecasting applications. For any given model, the monitoring technique is based on a comparison of the predictive ability of the model, measured by the observed values of predictive densities, with that of a single alternative. The alternative is…

正态模型中的筛选AI 解读

SUMMARY An individual is deemed ‘successful’ if the value of a certain measurement of interest Y lies in some given specification region. In situations in which Y is difficult to measure, the individuals may be screened using a correlated variable X which is easier to measure. The motivation behind screening is to try to increase the proportion of 'successes' by eliminating those individuals who are unlikely to be successful. Most approaches, except for very large sample…

稀疏乘积多项分布拟合优度统计量的渐近正态性AI 解读

SUMMARY The asymptotic distribution of the Pearson X 2 and likelihood ratio G 2 goodness-of-fit statistics is derived for k independent, non-identically distributed multinomials, as k approaches infinity, with expected cell frequencies bounded. The application is to large datasets of counts with many zero cells. Conditions are given under which the limiting distributions are normal for originating probabilities (i) known and (ii) dependent on a common, finite-dimensional…

区分时间序列中的异常值类型AI 解读

SUMMARY Distinguishing an outlier in a time series arising through measurement error from one arising through a perturbation of the underlying system can be of use in data validation. In this paper a method of testing for the presence of an outlier of unknown type is proposed. Then the properties of a rule based on the likelihood ratio which attempts to distinguish the two types of outlier are examined and compared with those of the corresponding Bayes rules. An example…

预测似然推断及其应用AI 解读

SUMMARY Conditional and marginal predictive likelihood are defined and used in predicting unobserved or missing data. A distinction is made between predictive and estimative goals of a data analysis. Such methodology and distinctions are illustrated in the context of outlier theory and mixed model ANOVA.

分组与未分组数据回归模型中最大似然估计的存在性AI 解读

SUMMARY In general, concavity of the log likelihood alone does not imply that the MLE exists always. For a class of linear regression models for grouped and ungrouped data, a necessary and sufficient condition is obtained for the existence of the maximum likelihood estimator. This condition has an intuitively simple interpretation. Further, it turns out that there are similar necessary and sufficient conditions for the existence of maximum likelihood estimates for a number…

回归中观测影响的决策理论度量AI 解读

SUMMARY A Bayesian decision-theoretic framework is used to define the influence of observations when fitting a regression model to data. Measures assessing an observation's influence on the posterior risk depend on the specification of the underlying loss function and prior assumptions. Illustrations are given for normal linear regression models.

基于标准化间距的拟合优度检验AI 解读

SUMMARY Normalized spacings provide useful tests of fit for many suitably regular continuous distributions; attractive features of the tests are that they can be used with unknown parameters and also with samples which are censored (Type 2) on the left and/or right. A transformation of the spacings leads, under the null hypothesis, to a set of z-values in (0, 1); however, these are not uniformly distributed except for spacings from the exponential or uniform distributions.…

图像恢复中的若干平滑技术AI 解读

SUMMARY The problem is considered of restoring a blurred and/or noisy image using various regularization prescriptions. Preliminary work concerns the invertibility of point spread functions and the construction of a stochastic model for images. A simple linear regularization procedure is introduced, as well as the special cases of constrained deconvolution, maximum entropy restoration and least-squares filtering. Optimal choices for the degree of smoothing are obtained for…

模糊先验信息下非齐次泊松过程的贝叶斯因子AI 解读

SUMMARY The calculation of Bayes factors for rival parametric models of non-homogeneous Poisson processes is considered. If vague prior information for the model parameters is represented by limiting improper prior forms, then the resulting Bayes factor is defined only up to a multiplicative constant. It is noted that the procedure proposed by Spiegelhalter and Smith (1982) does not provide any solution to the problem of assigning the constant if the priors are…

允许非连续观测的回归—ARMA时间序列模型精确极大似然估计AI 解读

SUMMARY An explicit procedure is given to obtain the exact maximum likelihood estimates of the parameters in a regression model with ARMA time series errors with possibly nonconsecutive data. The method is based on an innovation transformation approach from which an explicit recursive procedure is derived for the efficient calculation of the exact likelihood function and associated derivatives. The innovations and associated derivatives are used to develop a modified…

受噪声污染图像的统计分析AI 解读

SUMMARY A continuous two-dimensional region is partitioned into a fine rectangular array of sites or “pixels”, each pixel having a particular “colour” belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that…

摘要暂缺

NEAR(2) 模型的最大似然估计AI 解读

SUMMARY The NEAR(2) model is a model for nonlinear time series with exponential marginals. It formed the subject of a recent discussion paper by Lawrance and Lewis. We explore the possibility of maximum likelihood estimation with particular reference to the difficulties created by discontinuities in the likelihood function. Two exploratory techniques are proposed for resolving those difficulties. This note is an expanded version of a contribution presented orrally at the…

模糊先验信息下对数线性列联表模型的贝叶斯因子札记AI 解读

SUMMARY The approximate Bayes factor, B 01, for log-linear contingency table models proposed by Spiegelhalter and Smith (1982) is indeterminate if any of the cell frequencies is zero. It is noted that use of a standard Jeffreys prior overcomes this difficulty. It is pointed out that – 2 log B 01 is approximately equivalent to Schwarz's (1978) model selection criterion in large samples.

具有调整正交性的行列设计中行间与列间信息的恢复AI 解读

SUMMARY The analysis of row-column designs which satisfy the property of adjusted orthogonality is considered. For such designs a series of results are derived which relate the information matrix, its inverse, the estimator of the treatment effects and the adjusted treatment sum of squares to those of its component designs. It is also shown that estimators of the stratum variances required for the recovery of information from between rows and between columns can be obtained…

回归收缩预测量对历史与未来数据差异的稳健性AI 解读

SUMMARY Copas (1983) investigates the shrinkage associated with prediction in the usual linear multiple regression model and proposes using Stein-type predictors which anticipate this shrinkage. Assuming that the first two (population) moments of the regressor variables associated with individuals for which predictions are to be made coincide with the first two (sample) moments of those in the construction sample, preshrunk predictors give a uniformly lower prediction mean…

不依赖参数分布假设的取向统计AI 解读

SUMMARY Maximum likelihood estimation using the matrix von Mises-Fisher distribution in orientation statistics leads to unacceptably complicated likelihood equations, essentially because of the inconvenient form of the normalizing constant in the probability distribution. For the case of 3 × 2 or 3 × 3 orientations, the main cases of practical importance, an alternative approach is developed here by transforming the data into unsigned four-dimensional directions and using…

基于经验特征函数的指数分布对单调风险率备择检验AI 解读

SUMMARY A test of exponentiality is proposed which is consistent for alternatives with monotone failure rate. Derived as a weighted integral of the difference between the characteristic functions of the sample and of the exponential distribution, the scale-invariant statistic depends on the mean value of the exponential density function, evaluated at the sample observations. The power of the test is similar to that of the Gini test of Gail and Gastwirth (1978b), and both…

圆心与半径若干最小二乘估计量的统计性质AI 解读

SUMMARY This paper examines the statistical behaviour of some least squares estimators of the centre and radius of a circle. Two error models are used. The asymptotic consistency of the estimators is investigated. Where asymptotic consistency is established, asymptotic covariance matrices are obtained. A small sample simulation study gives results showing the same pattern as those of the asymptotic theory.

部分线性模型中的样条平滑AI 解读

SUMMARY Suppose that Yi = X'iβ + f(ti) + εi, 1 ≤ i ≤ n, where β, f, and εi are unknown, but the m-th derivative of f is square integrable. Estimates of β and f are given which minimize the sum of the residual sum of squares and a roughness penalty. It is shown that these estimates are Bayes under a diffuse prior on β and f, and that, under mild conditions on Xi, ti, εi, and the roughness penalty, the estimate of β is consistent and asymptotically normal.

病例—对照或选择依赖抽样下的 Logistic 模型拟合AI 解读

SUMMARY There has been a great deal of interest in recent years in fitting logistic and log-linear models to tables of population counts estimated from survey data. Since maximum likelihood methods are not available in general for complex survey designs, most work has concentrated on adapting standard methods developed for multinomial sampling. Maximum likelihood methods have been developed for some special designs, however, and we might expect ad hoc methods to be less…

利用未分类数据改进混合分布成分密度的非参数估计AI 解读

SUMMARY We present a very simple, utilitarian technique for combining categorized and uncategorized data to construct a nonparametric estimator of a component mixture density. The method can be used for a wide class of estimators, and provides a reduction in the variance compared with the estimator based solely on categorized data.

合并比率估计量与合并回归估计量的方差估计AI 解读

SUMMARY A class of variance estimators including the standard ones, for the combined ratio estimator and for the combined regression estimator, is proposed. Optimal variance estimators in terms of minimizing the mean square error are obtained. Both model-free and model-dependent comparison of some standard variance estimators is made. For the combined ratio estimator, a new formula for the second order expansion of its mean square error is derived; the jackknife variance…