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论贝叶斯稳态预测模型AI 解读

Summary A recent criterion of Smith (1979) seeks to generalize the steady forecasting model of Harrison and Stevens (1976) to take account of non-normality in the observation and system variables. In this note, predictive distributions and forecasts corresponding to quadratic and step loss functions are examined when the observation variable has a distribution belonging to the exponential family. It is shown that Smith's generalized model does not always yield forecasts…

某类多元正态概率的近似方法AI 解读

Summary In models of disease transmission, in which liability to disease is assumed to be normally distributed, the problem arises of calculating the probability that a given member of a group of individuals will contract the disease conditional on the other members exceeding some threshold. The special case in which the truncated variables are uncorrelated with each other occurs frequently and we consider here an approximation, based on a Gram-Charlier expansion, for the…

生存时间数据的经验贝叶斯分析AI 解读

Summary An empirical Bayes analysis of life-time data is described. The paper examines and extends the model discussed by Kalbfleisch (1978) in which the cumulative hazard function is treated as a gamma process. It is shown that the results obtained from the model by using grouped data (the usual case in practice) are more satisfactory than those obtained using continuous data. The paper also shows that a parameter representing the variability of the underlying gamma process…

联合分布极限定理及其在线性符号秩统计量中的应用札记AI 解读

Summary When investigating the limiting joint distribution of a pair of random variables, it is possible to proceed by studying the associated marginal and conditional distributions. A useful extension of some previous work in this area of Sethuraman is presented by considering the important case when one is conditioning on a lattice-type random variable. The results are applied to obtain, in a simple manner, the limiting distribution of a linear-signed rank statistic.

比较两个正态总体均值的渐近贝叶斯序贯检验AI 解读

Summary We consider sequential tests to decide whether the difference between the means of two normal populations is negative or positive. A Bayesian formulation is adopted, with costs of sampling which differ for the two populations and depend on the difference between the means. The asymptotic “shape”, in the sense of Schwarz (1962), of the Bayes continuation region is found, and this is used to derive an asymptotically Bayes test. A number of asymptotic optimality…

可靠性分析中一类多项分布的最大似然估计AI 解读

Summary Let Xi, i = 1, …,k be independent Bernoulli variables, with Xi ~ B(1, pi). Let Y = σ Xi, and consider a multinomial experiment based on n independent, identically distributed observations Y 1,…, Yn. This model is identifiable in the ordered parameter vector (p (1),…, p (k)), where p(i -1) ≤ p(i), and arises in reliability experiments in which k components in parallel have potentially different probabilities of failure. The family of multinomial distributions with the…

使用分组数据估计回归模型的最大似然方法札记AI 解读

Summary The estimation of parameters for a class of regression models using grouped or censored data is considered. It is shown that with a simple reparameterization some commonly used distributions, such as the normal and extreme value, result in a log-likelihood which is concave with respect to the transformed parameters. Apart from its theoretical implications for the existence and uniqueness of maximum likelihood estimates, this result suggests minor changes to some…

某类谱密度模型的参数估计程序AI 解读

Summary Let {X(t)} be a Gaussian stationary process with mean zero and true spectral density g(x). We shall fit a certain spectral model f θ (x) for this process, and propose an estimate of θ, say θ^n, by minimizing a criterion D{f θ , g), which measures the nearness of f θ (x) to g(x). Also we shall derive the asymptotic distribution of θ^n. For the case of some appropriate spectral parametrization of f θ (x) we show that θ^n can be expressed in an explicit form.…

样本时空自相关函数的方差AI 解读

Summary An important part of the diagnostic checking of space-time autoregressive moving average (starma) models is testing the temporal independence of the residuals. In the context of the three-stage modelling procedure, such a test is based on the sample space-time autocorrelation function. This paper developes approximate variances of the sample space-time autocorrelation function when the underlying process is white noise, which are needed to test significance of the…

经验特征函数方法的效率AI 解读

Summary The asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions.

Summary A technique for using kernel density estimates to investigate the number of modes in a population is described and discussed. The amount of smoothing is chosen automatically in a natural way.

多变量线性关系：最大似然估计与回归界限AI 解读

Summary The well known result that, when the ratio of error variances is specified in normal theory bivariate linear relationships, the maximum likelihood estimator of the slope parameter takes the same form for both structural and functional relationships is extended to the multivariate case. Furthermore, it is well known that in the bivariate case the estimator of the slope is bounded by the two regression estimators. Analogous results are derived for the multivariate…

结构对称性下矩阵分布所诱导的不变分布AI 解读

Summary Let Y(n x m) be a random matrix in the space F n x m of real matrices having location-scale parameters (θ, Ω) such that (i) θ belongs to a linear subspace M of F n x m; (ii) the distribution L(Y) exhibits a type of structural symmetry; and (iii) a certain transformation T(Y) is translation-invariant with respect to M and is invariant under changes of scale. Then the distribution L{T(Y)} is invariant for all underlying symmetric distributions L(Y). The types of…

关于若干抽样策略比较的一则札记AI 解读

Summary In this note we compare strategies H 1, H 2 and H 3 under a commonly used superpopulation model, where H1 consists of a πPS scheme and the Horvitz–Thompson (HT) estimator; H 2 consists of the Midzuno–Sen scheme and the corresponding HT estimator and H 3 is the Rao–Hartley–Cochran strategy. We first show that the sufficient condition for H 1 to be superior to H 2, due to Chaudhuri (1976), can never hold. We then suggest an alternative sufficient condition which is an…

二项响应模型中最大似然估计量的存在性AI 解读

Summary Necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response (this includes Logit and Probit) models.

多参数稳态演化模型AI 解读

SUMMARY This paper generalizes and extends the idea of a steady evolution of a time series to multiparameter processes with any observational distribution. Particular examples of such processes are given. These include the multivariate steady process, univariate normal processes where the observational variance is unknown and series of multinomial observations with a steady model on the cell probabilities.

双线性时间序列模型理论AI 解读

SUMMARY The theory of bilinear time series models is considered in this paper. The sufficient conditions for asymptotic stationarity of the bilinear time series models are derived, and the expressions for the variance and covariance are obtained. The conditions for the invertibility of the model are also included. The estimation of the parameters of the scalar bilinear time series model is considered. The bilinear models are fitted to sunspot numbers and also to a P-wave of…

季节移动平均模型中滞后缺项检验的一则注记AI 解读

SUMMARY A Lagrange multiplier test is suggested as an alternative to the procedure proposed by Godolphin for testing for gaps in a moving average model. It is shown to have more desirable statistical properties.

多变量ARMA时间序列模型中残差自相关的分布AI 解读

SUMMARY The large-sample distribution of the multivariate residual autocorrelations in the vector arma model is derived. This result is somewhat less complicated for the vector autoregressive model. A new multivariate portmanteau test for checking the adequacy of fitted vector arma models is developed. A simulation study shows that a simple modification of the portmanteau test improves its accuracy in small samples.

多元时间序列模型的拉格朗日乘子检验AI 解读

SUMMARY Generalizing Hosking (1980a), the Lagrange-multiplier test procedure is applied to hypotheses concerning multivariate autoregressive moving-average time-series models. The portmanteau and Quenouille goodness-of-fit tests for multivariate processes are derived in this manner and three other tests are obtained for multivariate moving-average models.

用于非椭圆对称多元数据建模的分布族AI 解读

SUMMARY The paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation. We present a relatively simple family of distributions for use in describing data which are not elliptically symmetric. Properties of the family are discussed and it is shown that multivariate Pareto, Burr and Logistic distributions are special cases. In addition, simulation methods for applications in Monte Carlo robustness studies are…

降秩回归与典型分析AI 解读

SUMMARY We show that maximum-likelihood analysis of the reduced-rank regression model exploits a fundamental inequality result of matrix theory when a normally distributed error structure with unknown covariance is assumed. This approach closely parallels the corresponding analysis when the covariance matrix is known (Davies and Tso, 1980) and demonstrates straightforwardly the intimate connection between reduced-rank regression and canonical analysis. A geometric…

变换与刀切法AI 解读

SUMMARY Whether to jackknife a parameter estimate or some function of it has in the past relied on recommendations based on folklore rather than statistical analyses. This paper puts the jackknifed estimator into the context of finding a least squares estimator from a model involving a location parameter with additive “pseudo” errors. Obtaining and interpreting confidence intervals from the partitioning of the “total” sum of squares into “residual” sum of squares, plus a sum…