AbstractThis article develops a novel estimation framework for the multithreshold accelerated failure time model, which has distinct linear forms within different subdomains. One major challenge is to determine the number of threshold effects. We first show the selection consistency of a modified Bayesian information criterion under mild conditions. It is useful sometimes but heavily depends on the penalization magnitude, which usually varies from the model configuration and data distribution. To address this issue, we leverage a cross‐validation criterion alongside an order‐preserved sample‐splitting scheme to yield a consistent estimation. The new criterion is completely data driven without additional parameters and thus robust to model setting and data distributions. The asymptotic properties for the parameter estimates are also carefully established. Additionally, we propose an efficient score‐type test to examine the existence of threshold effects. The new statistic is free of estimating any potential threshold effects and is thus suitable for multithreshold scenarios. Numerical experiments validate the reliable finite‐sample performance of our methodologies, which corroborates the theoretical results.

AbstractIn a variety of experimental settings there is an interest in comparing pairs–of–treatments. Such experiments usually address one of the following two scientific questions: (1) is there a difference within any of the selected pairs of treatments? or (2) is there a difference within all of the selected pairs of treatments? In this article, we propose max–min optimal designs for testing the above hypotheses using a graph‐based game theoretic approach. Some of the max–min designs obtained are well known, but not recognized as optimal, others are novel and provide an improvement over naive designs.

AbstractAs a commonly used nonparametric model to overcome the curse of dimensionality, the additive model continually attracts attentions of researchers. Our recent work (He et al., 2022) proposed to reduce the number of unknown functions to be estimated through learning an adaptive subspace shared by the additive component functions. Equipped with an efficient algorithm, our proposed reduced additive model outperforms the state‐of‐the‐art alternatives in numerical studies. However, the asymptotic properties of the proposed estimators have not been explored and the empirical findings are short of theoretical explanation. In this work, we fill in the theoretical gap by showing the resulting estimator has faster convergence rate than the estimation without subspace learning; and this is true even when the reduced additive model is only an approximation, provided that the subspace approximation error is small. Moreover, the proposed method is able to consistently identify the relevant predictors. The developed theoretical results back up the earlier empirical findings.

AbstractStepped wedge cluster randomized experiments (SW‐CREs) represent a class of unidirectional crossover designs. Although SW‐CREs have become popular, definitions of estimands and robust methods to target estimands under the potential outcomes framework remain insufficient. To address this gap, we describe a class of estimands that explicitly acknowledge the multilevel data structure in SW‐CREs and highlight three typical members of the estimand class that are interpretable. We then introduce four analysis of covariance (ANCOVA) working models to achieve estimand‐aligned analyses with covariate adjustment. Each ANCOVA estimator is model‐assisted, as its point estimator is consistent even when the working model is misspecified. Under the stepped wedge randomization scheme, we establish the finite population Central Limit Theorem for each estimator. We study the finite‐sample operating characteristics of the ANCOVA estimators in simulations and illustrate their application by analyzing the Washington State Expedited Partner Therapy study.

AbstractIn linear least squares regression there exists a simple decomposition of the effect of an exposure on an outcome into two parts in the presence of an intermediate variable. This decomposition is described and then analogous decompositions for other models are examined, namely for logistic regression and proportional hazards models.

AbstractWe propose a model to address the overlooked problem of node clustering in simple hypergraphs. Simple hypergraphs are suitable when a node may not appear multiple times in the same hyperedge, such as in co‐authorship datasets. Our model generalizes the stochastic blockmodel for graphs and assumes the existence of latent node groups and hyperedges are conditionally independent given these groups. We first establish the generic identifiability of the model parameters. We then develop a variational approximation Expectation‐Maximization algorithm for parameter inference and node clustering, and derive a statistical criterion for model selection. To illustrate the performance of our R package HyperSBM, we compare it with other node clustering methods using synthetic data generated from the model, as well as from a line clustering experiment and a co‐authorship dataset.