Electronic Journal of Statistics最新文献

Partly interval-censored data, comprising exact and intervalcensored observations, are prevalent in biomedical, clinical, and epidemiological studies. This paper studies a flexible class of the semiparametric Cox-Aalen transformation models for regression analysis of such data. These models offer a versatile framework by accommodating both multiplicative and additive covariate effects and both constant and time-varying effects within a transformation, while also allowing for potentially time-dependent covariates. Moreover, this class of models includes many popular models such as the semiparametric transformation model, the Cox-Aalen model, the stratified Cox model, and the stratified proportional odds model as special cases. To facilitate efficient computation, we formulate a set of estimating equations and propose an Expectation-Solving (ES) algorithm that guarantees stability and rapid convergence. Under mild regularity assumptions, the resulting estimator is shown to be consistent and asymptotically normal. The validity of the weighted bootstrap is also established. A supremum test is proposed to test the time-varying covariate effects. Finally, the proposed method is evaluated through comprehensive simulations and applied to analyze data from a randomized HIV/AIDS trial.

Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point estimates for the estimated graph can result in poor replicability without accompanying uncertainty estimates. In fields such as psychology, where the lack of replicability is a major concern, there is a growing need for methods that can address this issue. In this paper, we focus on the Gaussian graphical model. We introduce a selective inference method to attach uncertainty estimates to the selected (nonzero) entries of the precision matrix and decide which of the estimated edges must be included in the graph. Our method provides an exact adjustment for the selection of edges, which when multiplied with the Wishart density of the random matrix, results in valid selective inferences. Through the use of externally added randomization variables, our adjustment is easy to compute, requiring us to calculate the probability of a selection event, that is equivalent to a few sign constraints and that decouples across the nodewise regressions. Through simulations and an application to a mobile health trial designed to study mental health, we demonstrate that our selective inference method results in higher power and improved estimation accuracy.

In this manuscript, we study scalar-on-distribution regression; that is, instances where subject-specific distributions or densities are the covariates, related to a scalar outcome via a regression model. In practice, only repeated measures are observed from those covariate distributions and common approaches first use these to estimate subject-specific density functions, which are then used as covariates in standard scalar-on-function regression. We propose a simple and direct method for linear scalar-on-distribution regression that circumvents the intermediate step of estimating subject-specific covariate densities. We show that one can directly use the observed repeated measures as covariates and endow the regression function with a Gaussian process prior to obtain a closed form or conjugate Bayesian inference. Our method subsumes the standard Bayesian non-parametric regression using Gaussian processes as a special case, corresponding to covariates being Dirac-distributions. The model is also invariant to any transformation or ordering of the repeated measures. Theoretically, we show that, despite only using the observed repeated measures from the true density-valued covariates that generated the data, the method can achieve an optimal estimation error bound of the regression function. The theory extends beyond i.i.d. settings to accommodate certain forms of within-subject dependence among the repeated measures. To our knowledge, this is the first theoretical study on Bayesian regression using distribution-valued covariates. We propose numerous extensions including a scalable implementation using low-rank Gaussian processes and a generalization to non-linear scalar-on-distribution regression. Through simulation studies, we demonstrate that our method performs substantially better than approaches that require an intermediate density estimation step especially with a small number of repeated measures per subject. We apply our method to study association of age with activity counts.

The marginal inference of an outcome variable can be improved by closely related covariates with a structured distribution. This differs from standard covariate adjustment in randomized trials, which exploits covariate-treatment independence rather than knowledge on the covariate distribution. Yet it can also be done robustly against misspecification of the outcome-covariate relationship. Starting with a standard estimating function involving only the outcome, we first use a working regression model to compute its conditional expectation given the covariates, and then remove the uninformative part under the covariate distribution model. This effectively projects the initial function onto the joint tangent space of the full data, thereby achieving local efficiency when the regression model is correct. Importantly, even with a faulty working model, the estimator remains unbiased as the subtracted term is always asymptotically centered. Further improvement is possible if the outcome distribution also has its own structure. To demonstrate the process, we consider three examples: one with fully parametric covariates, one with a covariate following a partial parametric model against others, and another with mutually independent covariates.

Under model misspecification, it is known that Bayesian posteriors often do not properly quantify uncertainty about true or pseudo-true parameters. Even more fundamentally, misspecification leads to a lack of reproducibility in the sense that the same model will yield contradictory posteriors on independent data sets from the true distribution. To define a criterion for reproducible uncertainty quantification under misspecification, we consider the probability that two credible sets constructed from independent data sets have nonempty overlap, and we establish a lower bound on this overlap probability that holds whenever the credible sets are valid confidence sets. We prove that credible sets from the standard posterior can strongly violate this bound, indicating that it is not internally coherent under misspecification. To improve reproducibility in an easy-to-use and widely applicable way, we propose to apply bagging to the Bayesian posterior ("BayesBag"); that is, to use the average of posterior distributions conditioned on bootstrapped datasets. We motivate BayesBag from first principles based on Jeffrey conditionalization and show that the bagged posterior typically satisfies the overlap lower bound. Further, we prove a Bernstein-Von Mises theorem for the bagged posterior, establishing its asymptotic normal distribution. We demonstrate the benefits of BayesBag via simulation experiments and an application to crime rate prediction.