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拓展经验似然的适用范围AI 解读

This article extends the scope of empirical likelihood methodology in three directions: to allow for plug-in estimates of nuisance parameters in estimating equations, slower than $\sqrt{n}$-rates of convergence, and settings in which there are a relatively large number of estimating equations compared to the sample size. Calibrating empirical likelihood confidence regions with plug-in is sometimes intractable due to the complexity of the asymptotics, so we introduce a…

贝叶斯非参数推断的分位数金字塔AI 解读

Pólya trees fix partitions and use random probabilities in order to construct random probability measures. With quantile pyramids we instead fix probabilities and use random partitions. For nonparametric Bayesian inference we use a prior which supports piecewise linear quantile functions, based on the need to work with a finite set of partitions, yet we show that the limiting version of the prior exists. We also discuss and investigate an alternative model based on the…

回归模型中平均风险的最小化AI 解读

Most model selection mechanisms work in an “overall” modus, providing models without specific concern for how the selected model is going to be used afterward. The focused information criterion (FIC), on the other hand, is geared toward optimum model selection when inference is required for a given estimand. In this paper the FIC method is extended to weighted versions. This allows one to rank and select candidate models for the purpose of handling a range of similar tasks…

Cox 风险回归模型的聚焦信息准则与模型平均AI 解读

This article is concerned with variable selection methods for the Cox proportional hazards regression model. Including excessive covariates causes extra variability and inflated confidence intervals for regression parameters; thus regimes for discarding the less informative ones are needed. Our framework has p covariates designated as “protected,” while variables from a further set of q covariates are examined for possible inclusion or exclusion. We develop a focused…

后验预测 p 值的后处理校准AI 解读

This article addresses issues of model criticism and model comparison in Bayesian contexts, and focuses on the use of the so-called posterior predictive p values (ppp). These involve a general discrepancy or conflict measure and depend on the prior, the model, and the data. They are used in statistical practice to quantify the degree of surprise or conflict in data and to compare different combinations of prior and model. The distribution of such ppp values is far from…

频率学派模型平均估计量AI 解读

The traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen in advance, without acknowledging the additional uncertainty introduced by model selection. This often means underreporting of variability and too optimistic confidence intervals. We build a general large-sample likelihood apparatus in which limiting distributions and risk properties of estimators post-selection as well as of model average estimators are…

聚焦信息准则AI 解读

A variety of model selection criteria have been developed, of general and specific types. Most of these aim at selecting a single model with good overall properties, for example, formulated via average prediction quality or shortest estimated overall distance to the true model. The Akaike, the Bayesian, and the deviance information criteria, along with many suitable variations, are examples of such methods. These methods are not concerned, however, with the actual use of the…

论贝叶斯一致性AI 解读

Summary We consider a sequence of posterior distributions based on a data-dependent prior (which we shall refer to as a pseudoposterior distribution) and establish simple conditions under which the sequence is Hellinger consistent. It is shown how investigations into these pseudo posteriors assist with the understanding of some true posterior distributions, including Pólya trees, the infinite dimensional exponential family and mixture models.

以参数估计为起点的非参数密度估计AI 解读

The traditional kernel density estimator of an unknown density is by construction completely nonparametric in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities, for example, the normal, while not losing much in precision when the true density is…

正态模型能够容忍多大程度的 t 分布偏离AI 解读

Suppose that the normal model is used for data Y 1,…, Y n, but that the true distribution is a t distribution with location and scale parameters ζ and σ and m degrees of freedom. The normal model corresponds to m = ∞. Using a local asymptotic framework where m is allowed to increase with n, two classes of estimands are identified. One small class, which in particular contains the functions of ζ alone, is affected by t-ness only to the second order, and maximum likelihood…

估计量偏离目标值的最后时点与累计次数AI 解读

Suppose $\hat{\theta}_n$ is a strongly consistent estimator for $\theta_0$ in some i.i.d. situation. Let $N_\varepsilon$ and $Q_\varepsilon$ be, respectively, the last $n$ and the total number of $n$ for which $\hat{\theta}_n$ is at least $\varepsilon$ away from $\theta_0$. The limit distributions for $\varepsilon^2N_\varepsilon$ and $\varepsilon^2Q_\varepsilon$ as $\varepsilon$ goes to zero are obtained under natural and weak conditions. The theory covers both parametric…

基于贝塔过程的生命历程数据非参数贝叶斯估计AI 解读

Several authors have constructed nonparametric Bayes estimators for a cumulative distribution function based on (possibly right-censored) data. The prior distributions have, for example, been Dirichlet processes or, more generally, processes neutral to the right. The present article studies the related problem of finding Bayes estimators for cumulative hazard rates and related quantities, w.r.t. prior distributions that correspond to cumulative hazard rate processes with…

基于累积风险率的生命历程数据模型拟合优度检验AI 解读

To check the validity of an assumed parametric model for survival data, one may compare $\hat{A}(t)$, the nonparametric Nelson-Aalen plot of the cumulative hazard rate, with $A(t, \hat{\theta})$, the estimated parametric cumulative hazard rate, $\hat{\theta}$ being for example the maximum likelihood estimator. Convergence in distribution of $\sqrt n (\hat{A}(t) - A(t, \hat{\theta}))$ and more general processes is studied in the present paper, employing the general framework…