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二次支撑风险下的一致模型选择准则AI 解读

In this paper, we study asymptotic properties of model selection criteria for high-dimensional regression models where the number of covariates is much larger than the sample size. In particular, we consider a class of loss functions called the class of quadratically supported risks which is large enough to include the quadratic loss, Huber loss, quantile loss and logistic loss. We provide sufficient conditions for the model selection criteria, which are applicable to the…

超高维非凸惩罚回归的校准AI 解读

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is…

高维情形下的平滑截断绝对偏差估计AI 解读

The smoothly clipped absolute deviation (SCAD) estimator, proposed by Fan and Li, has many desirable properties, including continuity, sparsity, and unbiasedness. The SCAD estimator also has the (asymptotically) oracle property when the dimension of covariates is fixed or diverges more slowly than the sample size. In this article we study the SCAD estimator in high-dimensional settings where the dimension of covariates can be much larger than the sample size. First, we…

将随机效应模型置于生存分析框架AI 解读

Summary Logistic random-effects models are often employed in the analysis of correlated binary data. However, fitting these models is challenging, since the marginal distribution of the response variables is analytically intractable. Often, the random effects are treated as missing data for constructing traditional data augmentation algorithms. We create a novel alternative data augmentation scheme that simplifies the likelihood-based inference for logistic random-effects…

比例风险模型的 Bernstein–von Mises 定理AI 解读

We study large sample properties of Bayesian analysis of the proportional hazard model with neutral to the right process priors on the baseline hazard function. We show that the posterior distribution of the baseline cumulative hazard function and regression coefficients centered at the maximum likelihood estimator is jointly asymptotically equivalent to the sampling distribution of the maximum likelihood estimator.

非参数右删失模型中的 Bernstein–von Mises 定理AI 解读

In the recent Bayesian nonparametric literature, many examples have been reported in which Bayesian estimators and posterior distributions do not achieve the optimal convergence rate, indicating that the Bernstein–von Mises theorem does not hold. In this article, we give a positive result in this direction by showing that the Bernstein–von Mises theorem holds in survival models for a large class of prior processes neutral to the right. We also show that, for an arbitrarily…

比例风险模型的贝叶斯自助法AI 解读

We propose two Bayesian bootstrap extensions, the binomial and Poisson forms, for proportional hazards models. The binomial form Bayesian bootstrap is the limit of the posterior distribution with a beta process prior as the amount of the prior information vanishes, and thus can be considered as a default nonparametric Bayesian analysis. It is also the same as Lo's Bayesian bootstrap for censored data when covariates are absent. The Poisson form Bayesian bootstrap is…

比例风险模型的贝叶斯分析AI 解读

This paper is concerned with Bayesian analysis of the proportional hazard model with left truncated and right censored data. We use a process neutral to the right as the prior of the baseline survival function and a finite-dimensional prior is placed on the regression coefficient. We then obtain the exact form of the joint posterior distribution of the regression coefficient and the baseline cumulative hazard function. As a by-product, we prove the propriety of the posterior…

生存模型的后验一致性AI 解读

Ghosh and Ramamoorthi studied posterior consistency for survival models and showed that the posterior was consistent when the prior on the distribution of survival times was the Dirichlet process prior. In this paper,we study posterior consistency of survival models with neutral to the right process priors which include Dirichlet process priors. A set of sufficient conditions for posterior consistency with neutral to the right process priors are given. Interestingly, not all…

计数过程的非参数贝叶斯估计量AI 解读

This paper is concerned with nonparametric Bayesian inference of the Aalen’s multiplicative counting process model. For a desired nonparametric prior distribution of the cumulative intensity function, a class of Lévy processes is considered, and it is shown that the class of Lévy processes is conjugate for the multiplicative counting process model, and formulas for obtaining a posterior process are derived. Finally, our results are applied to several practically important…