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计量经济建模的统计基础AI 解读

Foreword David Hendry Preface Acknowledgements Part I. Introduction: 1. Econometric modelling, a preliminary view 2. Descriptive study of data Part II. Probability Theory: 3. Probability 4. Random variables and probability distributions 5. Random vectors and their distributions 6. Functions of random variables 7. The general notion of expectation 8. Stochastic processes 9. Limit theorems 10. Introduction to asymptotic theory Part III. Statistical Inferences: 11. The nature…

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经验贝叶斯置信区间的构造方法AI 解读

Parametric empirical Bayes (EB) methods of point estimation date to the landmark paper by James and Stein (1961). Interval estimation through parametric empirical Bayes techniques has a somewhat shorter history, which was summarized by Laird and Louis (1987). In the exchangeable case, one obtains a “naive” EB confidence interval by simply taking appropriate percentiles of the estimated posterior distribution of the parameter, where the estimation of the prior parameters…

Remedian：适用于大型数据集的稳健平均方法AI 解读

It is often assumed that to compute a robust estimator on n data values one needs at least n storage elements (contrary to the sample average, that may be calculated with an updating mechanism). This is one of the main reasons why robust estimators are seldom used for large data sets and why they are not included in most statistical packages. We introduce a new estimator that takes up little storage space, investigate its statistical properties, and provide an example on…

删失对置信区间有效性的影响AI 解读

This article examines how the level of censoring affects the validity of confidence intervals constructed from an exponential maximum likelihood estimator under departures from an assumed exponential survival distribution. The motivation for this work is a simulation study by Emerson (1981) suggesting that under Weibull departures from exponentiality, validity of confidence intervals for median survival time improves as censoring increases. To see if this result holds…

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共同主成分及相关多元模型AI 解读

Preliminaries principal component analysis relationships between matrices common practical components proportional covariance matrices partial common components and common space analysis how different are several covariance matrices? numerical methods. Appendices: spectral decomposition of symmetric matrices some results from matrix algebra a fortran program for the fg algorithm.

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缺失数据下均值与协方差结构的伪极大似然估计AI 解读

A nonlinear mean- and covariance-structure model for one or more groups is constructed. The model subsumes the usual linear model considered in the literature. It is then shown how to estimate the parameters of the model and the asymptotic covariance matrix of the parameter estimates using pseudo-maximum likelihood (PML) estimation. The resulting estimates are strongly consistent under general regularity conditions, provided only that the model for the first two moments is…

最小平方中位数回归直线的计算与引导式拓扑扫描AI 解读

Given a set of data points pi = (xi, yi ) for 1 ≤ i ≤ n, the least median of squares regression line is a line y = ax + b for which the median of the squared residuals is a minimum over all choices of a and b. An algorithm is described that computes such a line in O(n 2) time and O(n) memory space, thus improving previous upper bounds on the problem. This algorithm is an application of a general method built on top of the topological sweep of line arrangements.

模块化非参数子生存分布估计AI 解读

This article describes new methods for estimating survival distributions based on nonparametric curve estimators. One approach improves the estimation of long-term survival rates. Simulation studies using Weibull and lognormal data show that even in the case found to be least favorable, the new method has less than one-seventh the prediction error of all conventional life-table (LT) or Kaplan–Meier (KM) estimators, even when the LT and KM techniques are optimized for the…

中位数无偏性与Pitman接近性AI 解读

Under certain conditions, a median unbiased estimator of a parameter is shown to be the Pitman-closest estimator within a certain class of estimators. For location, scale, or location-scale families of distributions, the class of equivariant estimators possesses some desirable properties; the median-unbiasedness of equivariant estimators is explored in the characterization of the Pitman closeness property. Illustrative examples bear fruitful implications of this…

帕累托数据的贝叶斯估计与预测AI 解读

Data from a classical Pareto distribution are to be used to make inferences about the inequality and precision parameters. In addition, it is desired to predict the behavior of further observations from the distribution. Three typical data configurations are considered (iid and two types of censoring). Dependent conjugate prior analyses are reviewed and are compared with an analysis involving independent priors for the inequality and precision parameters. It is argued that…

方向数据的自助法置信区域AI 解读

Methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p-dimensional unit vector X with an arbitrary unimodal distribution on the p sphere. The approach of this article differs from that of other authors in that it is based on pivotal statistics. A general pivotal method is introduced that produces a wide variety of confidence regions on general p-dimensional spheres; included are confidence cones and likelihood-based regions.…

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时期总生育率预测：微观动态新古典生育模型的时间序列性质AI 解读

"This article demonstrates the value of microdata for understanding the effect of wages on life cycle fertility dynamics. Conventional estimates of neoclassical economic fertility models obtained from linear aggregate time series regressions are widely criticized for being nonrobust when adjusted for serial correlation. Moreover, the forecasting power of these aggregative neoclassical models has been shown to be inferior when compared with conventional time series models…

状态空间模型中的平滑与插值AI 解读

A new result dealing with smoothing and interpolation in the state-space model is developed and explored. The result simplifies the derivation of existing smoothing algorithms and provides alternate forms that have analytic and practical computing advantages. The connection to signal extraction and interpolation is explored, and diffuse specifications are considered.

Cox 比例风险模型的稳健推断AI 解读

We derive the asymptotic distribution of the maximum partial likelihood estimator β for the vector of regression coefficients β under a possibly misspecified Cox proportional hazards model. As in the parametric setting, this estimator β converges to a well-defined constant vector β*. In addition, the random vector n 1/2(β – β*) is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated. The newly proposed robust covariance matrix…

通过边际分布建模分析多元不完整失效时间数据AI 解读

Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time observations. Each marginal distribution of the failure times is formulated by a Cox proportional hazards model. No specific structure of dependence among the distinct failure times on each subject is…

非加性多维分类数据的分析AI 解读

This article considers the problems of testing additivity and estimating σ2 in unreplicated multiway classifications. To model nonadditivity and jointly estimate σ2, the interaction parameter space must be restricted; otherwise the model is saturated. The parameterization we use is a multiway extension of the two-way multiplicative interaction model of Mandel (1971) and Johnson and Graybill (1972a). For example, in a three-way classification, we model interaction as θijk =…

贝叶斯边际推断AI 解读

A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be quite accurate in a number of special cases. There are similarities with the profile likelihood ideas originated by Kalbfleisch and…

基于观测间方向计数的分布无关多元符号检验AI 解读

Distribution-free tests are investigated for the one-sample multivariate location problem. Counts, called interdirections, which measure the angular distance between two observation vectors relative to the positions of the other observations, are introduced. These counts are invariant under nonsingular linear transformations and have a small-sample distribution-free property over a broad class of population models, called distributions with elliptical directions, which…