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连续谱回归：以交叉验证统一最小二乘、偏最小二乘与主成分回归AI 解读

SUMMARY The paper addresses the evergreen problem of construction of regressors for use in least squares multiple regression. In the context of a general sequential procedure for doing this, it is shown that, with a particular objective criterion for the construction, the procedures of ordinary least squares and principal components regression occupy the opposite ends of a continuous spectrum, with partial least squares lying in between. There are two adjustable ‘parameters’…

SUMMARY In a heteroscedastic linear regression model, the ordinary jackknife estimator of the asymptotic covariance matrix of the weighted least squares estimator is proved to be inconsistent. A modified jackknife procedure is proposed and shown to produce consistent estimators of the asymptotic covariance matrix. Finite sample performances of the jackknife, the modified jackknife and the customary S method are discussed. Some empirical results are also presented.

利用 EM 自身计算步骤实现快速改进AI 解读

SUMMARY The EM algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models. It is easy to apply in many problems and is stable but slow. The algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the Louis method is performed. Newton-type or other gradient methods are faster and provide error estimates but…

与 Weibull 分布相联系的一类多元分布AI 解读

SUMMARY A simple form of multivariate distribution is defined which, for certain parameter values, has Weibull marginals. The distribution has a single parameter governing association between the variates, which may be positive, negative or zero. The simple forms for marginal and conditional distributions, hazard functions and densities make it attractive for practical application and interpretation.

线性回归模型中若干误差协方差矩阵检验的最优性AI 解读

SUMMARY This paper adopts the approach of conditional distributions to investigate the optimality of some tests of the error covariance matrix in the linear regression model. Specifically, we show that point optimal tests, advocated by King and Evans and King, are the most powerful similar test. We also derive the locally best similar and the locally best unbiased similar tests. Finding the latter cumbersome to apply, we then propose the asymptotically best similar and the…

具有双指数分布噪声的 ARMA 模型AI 解读

SUMMARY The marginal and bivariate distributions of the observations generated from a standard autoregressive moving average scheme are derived, assuming the noise to have a double-exponential (Laplace) distribution. The distributions may differ substantially from their Gaussian counterparts. The AR(1) model with double-exponential noise is applied to a series of weekly measurements of sulphate concentration and is shown to give a significantly better fit when compared with…

离散参数可变的广义线性模型AI 解读

SUMMARY Generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean. It is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately. Mean and dispersion submodels are formulated for this, the dependent variable for the dispersion submodel being the deviance components of the mean submodel. The fact…

传递函数模型的估计与识别方法AI 解读

SUMMARY This paper proposes an approach to the simultaneous identification and estimation of transfer function models. An estimation procedure is advanced consisting of a sequence of four ordinary least squares calculations and the asymptotic properties of each step are presented, consistency and asymptotic efficiency being shown. A strategy for the identification of the model structure based on a selection criterion that arises naturally from the last step of the estimation…

边际似然在时间序列模型估计中的运用AI 解读

SUMMARY In the context of time series regression, with an error model of the ARIMA type, the fitting of the regression can seriously bias the ARIMA model parameter estimates. Moreover, choosing between different error models on the basis of the smallest residual variance may lead to incorrect selection with a high probability, even in samples of moderate size. The marginal likelihood procedure is considered as a solution to these problems and examples are presented in the…

回归中的方差函数估计：估计均值的影响AI 解读

SUMMARY We consider estimation of a variance function g in regression problems. Such estimation requires simultaneous estimation of the mean function f. We obtain clear results on the extent to which the smoothness of f influences best rates of convergence for estimating g. For example, in nonparametric regression with two derivatives on g, ‘classical' rates of convergence are possible if and only if the unknown f satisfies a Lipschitz condition of order 13 or more. If a…

空间点过程二阶强度加权积分的估计AI 解读

SUMMARY This paper considers the nonparametric estimation of the integral J=∫0Ttλ2(t)φ(t)dt where λ2(t) is the unknown second-order intensity function of a two-dimensional stationary isotropic point process observed in some region and φ(t) is known for t ϵ [0, T]. An unbiased estimator of J is derived, and a computationally fast approximation to it is proposed. The estimator is then used to obtain a kernel method for smoothing point process data, a new estimator of the…

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模拟阶数对 Monte Carlo 检验水平精度与功效的影响AI 解读

SUMMARY We discuss the effect of simulation order on level accuracy and power of Monte Carlo tests, in a very general setting. Both parametric problems, with or without nuisance parameters, and nonparametric problems are treated by a single unifying argument. It is shown that if the level of a Monte Carlo test is known only nominally, not precisely, then the level error of a Monte Carlo test is an order of magnitude less than that of the corresponding asymptotic test. This…

层级统计模型与广义似然比检验AI 解读

SUMMARY This paper deals with statistical inference for statistical models which have a nested structure. The emphasis here is on the use of a classical test of significance and on a confidence set construction approach for model identification, and the paper proposes a generalized likelihood ratio test with equal marginal error rate as a basic tool. The power performance of this test is characterized and some applications are illustrated.

二维列联表合并与卡方缩减原则AI 解读

SUMMARY The value of the chi-square statistic for homogeneity of rows and columns in a contingency table remains unchanged if the table is collapsed (grouped) over homogeneous rows and columns. The difference between the chi-square values pertaining to the original table and to the collapsed table (the ‘chi-square reduction‘) is shown to have a meaningful canonical decomposition which can guide the researcher in detecting homogeneous rows and columns. The methodology…

时间序列的留 K 法诊断AI 解读

SUMMARY We propose diagnostics for autoregressive integrated moving average (ARIMA) model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters. The use of leave-one-out diagnostics is a well-established tool in regression analysis. We demonstrate the efficacy of observation-deletion-based diagnostics for ARIMA models, addressing issues special to the time series setting. It is shown that the…

中期分析：重复置信区间方法AI 解读

SUMMARY Most medical trials are monitored for early evidence of treatment differences or harmful side-effects and many sequential methods have been proposed for this. Similarly, data collected in a prospective epidemiological study are likely to be reviewed periodically in the course of the study. The repeated confidence interval approach, which combines aspects of sequential estimation and testing, allows a full exploration of the data at each interim analysis and does not…

特征函数估计的切比雪夫多项式近似：若干理论补充AI 解读

SUMMARY Densities for the angle Θ = uX(mod 2π) and the cosine Y = cos(uX) can be expressed, through Fourier methods, in terms of the characteristic function of X. Thus, if X has a characteristic function of closed form, the parameters of its distribution may be estimated by maximum likelihood. The paper addresses the problems of estimability of asymmetric distributions and situations where the method may not apply.

利用辅助信息估计有限总体中位数AI 解读

SUMMARY This paper deals with the estimation, under simple random sampling, of a finite population median in the presence of an auxiliary variable. An estimator which is a simple modification of the ratio estimator for the mean is studied along with two other proposed estimators derived from a different approach. These estimators are applicable in situations where only the population median or a grouped frequency distribution of the auxiliary variable is known. On the basis…

白高斯时间序列中周期成分的检测AI 解读

SUMMARY A family of tests for periodic components in a white Gaussian series is proposed. The test is based on a statistic which is proportional to the ratio of the maximum periodogram to a trimmed mean of the periodograms. The asymptotic distributions of the statistics are obtained. It is shown that the proposed test and Fisher's test have the same asymptotic powers against the alternative of a sinusoidal wave at a non-zero Fourier frequency. The simulation results suggest…

配对取向统计量的球面回归AI 解读

SUMMARY The matched pairs section of the analysis of 3 times 3 orientation statistics in Prentice (1986) may be improved on by constructing a rotational regression model, an analogue of spherical regression. The results obtained are relatively simple consequences of the work of Chang and are therefore presented here for general orientation statistics—rigid orthogonal m frames in p dimensions—before application to the matched pairs of vectorcardiogram orientations (m = p = 3)…

自回归模型的递归估计AI 解读

SUMMARY This paper is concerned with the recursive estimation of autoregressive models, in particular the realtime determination of the order of such a specification. A model selection criterion based on the minimum description length principle due to Rissanen is discussed and strong consistency in the stationary situation is shown. Alternative criteria are also considered and modifications required to introduce forgetting when the procedures are implemented in the…

针对似然原则的一个反例AI 解读

SUMMARY A counter-example against the likelihood principle is strengthened and shown to hold also for a finite sample space.

多元时间序列的模型设定AI 解读

SUMMARY We propose a method to specify an appropriate yet parsimonious vector autoregressive moving average (ARMA) model for a given multivariate time series. By considering contemporaneous linear transformations of the vector process, we introduce the concept of scalar component models within the vector ARMA framework (a) to reveal possibly hidden simplifying structures of the process, (b) to achieve parsimony in parameterization and (c) to identify the exchangeable models.…