Abstract In this paper, we consider dependent competing risks using the Extended Marshall–Olkin model, where observation times are subject to censoring. The probabilistic properties of the survival copula associated with this model are examined, along with its application to the analysis of censored data. An estimation strategy using Bernstein polynomials for marginal distributions and joint survival probabilities is developed. The asymptotic normality of the proposed estimators is established under appropriate regularity conditions. The effectiveness of the proposed methodology is assessed through a simulation study using synthetic datasets and further validated with an application to real‐world data.

Abstract Harmonizable processes form a wide class of nonstationary processes, which admit a convenient Fourier analysis and have spectral distributions characterized by correlated components. They have been proven to be useful in many fields of application, e.g., in communication, seismology, EEG data analysis, etc. In this paper, we introduce a parametric form for harmonizable processes, namely Harmonizable Vector AutoRegressive and Moving Average models (HVARMA). In the same spirit as standard VARMA models, they are derived as a unique solution of a difference equation based on a properly defined concept of harmonizable noise. We exhibit their spectral characteristics and derive results for least‐squares parameter estimation in a fundamental case. We notably obtain, in some particular cases of the explosive regime, unusual asymptotic laws. Most importantly, we provide an effective way to generate realizations from those novel processes. Our modeling choice for harmonizable noise induces second‐order stationary dependencies among the components of the spectral distribution of the harmonizable time series. We choose to model them using a periodic stationary VARMA process, resulting in the so‐called HVARMA– model. We characterize its spectral properties and illustrate its ability to capture a vast range of nonstationary behaviors through examples of realizations using various models.

Abstract The Gaussian assumption is the most common and widely used distribution in statistical methodology. Various affine invariant tests for normality rely on the inverse of the covariance matrix and do not apply to high‐dimensional data. The Gaussian moments are equal to the specific values, which implies an exclusive quantitative relationship. This paper introduces two novel indices, the co‐third moment and the co‐fourth moment, to characterize the shape of the distribution relative to the high‐dimensional Gaussian family. Using these indices, two new tests with asymptotic properties under mild regularity conditions defining the subfamily for which tests are theoretically valid are proposed, which substantially avoid using the inverse covariance matrix and are easy to implement. By aggregating the strengths of the two tests and using the power enhancement technique, this study develops a more sensitive test of high‐dimensional normality. Numerical studies and real data analyses provide evidence that the proposed methods achieve well‐controlled size and competitive power, and illustrate their ability to detect departures from Gaussianity across different dimensional settings. The practical steps for empirically checking the regularity conditions are also discussed.

Abstract Hypothesis testing for fixed effects in linear mixed model is indispensable for investigating the utility of the predictors on response. However, when the dimension of covariates exceeds the sample size, the conventional frequentist methods designed for fixed dimensions fail completely. In this article, we develop a Bayesian‐motivated test for high‐dimensional linear mixed model to examine the significance of fixed effects in group. The proposed statistic is formulated as the ratio of two quadratic forms constructed from a sequence of independent but not identically distributed random variables. The null distribution of the proposed test statistic is derived through normality approximation for quadratic forms. To facilitate the implementation of the test, we introduce an innovative one‐step iteration method to determine the critical value. Additionally, the power function under local alternatives is derived under some mild conditions. In numerical experiments, we demonstrate the power performance in comparison with the existing method and the practical utility of the proposed method.

Abstract Nonresponse in probability sampling presents a long‐standing challenge in survey sampling, often necessitating simultaneous adjustments to address sampling and selection biases. We develop a statistical framework that explicitly models sampling weights as random variables and establish the semiparametric efficiency bound for the parameter of interest under nonresponse. This study investigates strategies for eliminating bias and effectively utilizing available information, extending beyond nonresponse issues to data integration with external summary statistics. The proposed estimators are characterized by their efficiency and double robustness. However, realizing full efficiency hinges on the accurate specification of underlying models. To enhance robustness against potential model misspecification, we expand double robustness to multiple robustness through a novel two‐step empirical likelihood approach. A numerical study evaluates the finite‐sample performance of our methods. Additionally, we apply these methods to a dataset from the National Health and Nutrition Examination Survey, effectively integrating summary statistics from the National Health Interview Survey.

Abstract In high dimensions, the relationship between covariates and a response variable becomes increasingly intricate, with different covariate components often displaying varying degrees of variability. This complex interplay of dependence, heterogeneity, and high dimensionality presents a significant challenge when investigating the effects of covariates on the response variable. To address this, we propose a novel marginal testing procedure based on kernel‐based conditional mean dependence, which can be implemented without requiring model assumptions. Theoretically, we establish the limiting normal distributions of the test statistic under both null hypotheses and local alternatives by asymptotically approximating a class of quadratic forms. We also examine the asymptotic relative efficiency of the proposed test against several state‐of‐the‐art alternatives. Our theoretical evaluations are conducted from two perspectives: a detailed analysis within a linear model framework and a comparison within a fully non‐parametric setting. The effectiveness and applicability of the proposed method are demonstrated through both simulation studies and real data analysis.

ABSTRACT Latent Gaussian models (LGMs) are a subset of Bayesian Hierarchical models where Gaussian priors, conditional on variance parameters, are assigned to all effects in the model. LGMs are employed in many fields for their flexibility and computational efficiency. However, practitioners find prior elicitation on the variance parameters challenging because of a lack of intuitive interpretation for them. Recently, several papers have tackled this issue by representing the model in terms of variance partitioning (VP) and assigning priors to parameters reflecting the relative contribution of each effect to the total variance. So far, the class of priors based on VP has been mainly applied to random effects and fixed effects separately. This work presents a novel standardization procedure that expands the applicability of VP priors to a broader class of LGMs, including both fixed and random effects. The practical advantages of standardization are demonstrated with simulated data and a real dataset on survival analysis.