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跨极端依赖类别的统一建模AI 解读

Summary Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for but can substantially impact subsequent extrapolation. Existing modelling solutions to…

极端事件的时空建模AI 解读

Summary Max-stable processes are the natural analogues of the generalized extreme value distribution when modelling extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of independent replications of random fields, and they are also suitable for the modelling of extreme measurements over high thresholds. The paper shows how a pairwise censored likelihood can be used for consistent estimation of the…

线性指数族中向量参数的精确方向性推断AI 解读

We consider inference on a vector-valued parameter of interest in a linear exponential family, in the presence of a finite-dimensional nuisance parameter. Based on higher-order asymptotic theory for likelihood, we propose a directional test whose p-value is computed using one-dimensional integration. The work simplifies and develops earlier research on directional tests for continuous models and on higher-order inference for discrete models, and the examples include…

Brown–Resnick 过程的复合似然估计AI 解读

Genton et al. (2011) investigated the gain in efficiency when triplewise, rather than pairwise, likelihood is used to fit the popular Smith max-stable model for spatial extremes. We generalize their results to the Brown–Resnick model and show that the efficiency gain is substantial only for very smooth processes, which are generally unrealistic in applications.

混合模型的鞍点近似AI 解读

Two-component mixture distributions with one component a point mass and the other a continuous density may be used as priors for Bayesian inference when sparse representation of an underlying signal is required. We show how saddlepoint approximation in such models can yield highly accurate quantiles for posterior distributions, and illustrate this numerically, using wavelet regression with point mass/Laplace and point mass/normal prior distributions.

多元极值的混合模型AI 解读

Summary The spectral density function plays a key role in fitting the tail of multivariate extre-mal data and so in estimating probabilities of rare events. This function satisfies moment con-straints but unlike the univariate extreme value distributions has no simple parametric form. Parameterized subfamilies of spectral densities have been suggested for use in applications, and non-parametric estimation procedures have been proposed, but semiparametric models for…

离散数据的改进似然推断AI 解读

Summary Discrete data, particularly count and contingency table data, are typically analysed by using methods that are accurate to first order, such as normal approximations for maximum likelihood estimators. By contrast continuous data can quite generally be analysed by using third-order procedures, with major improvements in accuracy and with intrinsic separation of information concerning parameter components. The paper extends these higher order results to discrete data,…

作为平滑器的鞍点近似AI 解读

This note investigates the sense in which saddlepoint approximations act as smoothers of discrete distributions. The discrete problem is embedded in a continuous model that closely matches it on the discrete sample space, with saddlepoint approximation yielding an inference that is almost exact for the continuous model. The same applies to conditional distributions. An example is given and implications for inference are discussed.

样本极值的局部似然平滑AI 解读

Summary Trends in sample extremes are of interest in many contexts, an example being environmental statistics. Parametric models are often used to model trends in such data, but they may not be suitable for exploratory data analysis. This paper outlines a semiparametric approach to smoothing sample extremes, based on local polynomial fitting of the generalized extreme value distribution and related models. The uncertainty of fits is assessed by using resampling methods. The…

离散化事件序列的若干模型AI 解读

A discretized series of events is a binary time series that indicates whether or not events of a point process in the line occur in successive intervals. Such data are common in environmental applications. We describe a class of models for them, based on an unobserved continuous-time discrete-state Markov process, which determines the rate of a doubly stochastic Poisson process, from which the binary time series is constructed by discretization. We discuss likelihood…

判别问题中bootstrap与交叉验证误判率估计的偏差和变异AI 解读

Simulation studies have shown that bootstrap and cross-validation estimators of aggregate error rate in discrimination problems have different properties, the former having less variability but greater bias. We show by use of a local alternative model that the main differences in bias and variability emerge only when the populations are close. In this context the bootstrap method has less variability but an order of magnitude greater bias than cross-validation.

摘要暂缺

配对数据中的处理效应异质性AI 解读

Data from matched pairs are often analysed under the assumption that treatment effects are homogeneous. We develop tests of this assumption, with Poisson and binomial examples. Mixture models for inference when overdispersion is present are investigated, with stress on matched pairs of counts.

判别问题中 bootstrap 与交叉验证误差率估计的偏差和变异性AI 解读

Simulation studies have shown that bootstrap and cross-validation estimators of aggregate error rate in discrimination problems have different properties, the former having less variability but greater bias. We show by use of a local alternative model that the main differences in bias and variability emerge only when the populations are close. In this context the bootstrap method has less variability but an order of magnitude greater bias than cross-validation.

摘要暂缺

偏差残差与正态分数图AI 解读

We discuss the use of normal order statistics plots, based on deviance residuals, to check distributional assumptions in regression models. Continuous and discrete error distributions are considered, as are censored data. Misspecified error distributions and discrimination between competing models are discussed, with an example.

偏差残差与正态分数图AI 解读

We discuss the use of normal order statistics plots, based on deviance residuals, to check distributional assumptions in regression models. Continuous and discrete error distributions are considered, as are censored data. Misspecified error distributions and discrimination between competing models are discussed, with an example.

广义线性模型中的近似条件推断AI 解读

SUMMARY Easily calculated and accurate approximations are developed to the conditional densities and distributions of sufficient statistics in generalized linear models with canonical link functions. They enable conditional inferences based on modified profile log-likelihoods and tail probabilities to be made using only the deviance and the variance matrix estimate based on fitted models. Examples are given in binary logistic regression and a log-linear model, and the…

摘要暂缺

近似预测似然AI 解读

A predictive likelihood is given which approximates both Bayes and maximum likelihood predictive inference by expansion of a posterior likelihood. This synthesizes and extends previous results and is widely applicable. The approximation usually differs from exact Bayes posterior predictive density by Op(n–2), and from exact predictive likelihood by Op(n–2) but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot…

近似预测似然AI 解读

A predictive likelihood is given which approximates both Bayes and maximum likelihood predictive inference by expansion of a posterior likelihood. This synthesizes and extends previous results and is widely applicable. The approximation usually differs from exact Bayes posterior predictive density by Op(n–2), and from exact predictive likelihood by Op(n–2) but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot…