ABSTRACT In this paper, we introduce a general theoretical framework for nonparametric hazard rate estimation using associated kernels, whose shapes depend on the point of estimation. Within this framework, we establish rigorous asymptotic results, including a second‐order expansion of the MISE, and a central limit theorem for the proposed estimator. We also prove a new oracle‐type inequality for both local and global adaptive bandwidth selection, extending the Goldenshluger‐Lepski method to the context of associated kernels. Our results propose a systematic way to construct and analyze new associated kernels. Finally, we show that the general framework applies to the Gamma kernel, and we provide several examples of applications on simulated data and experimental data for the study of aging.
ABSTRACT This article studies unsupervised transfer learning for a binary outcome, with labeled source data and unlabeled target covariates. The setting is motivated by cases where standard covariate‐shift and label‐shift assumptions are inadequate: group‐ or environment‐related features may vary jointly with the label across populations, while the remaining covariates remain conditionally stable given these features and the label. We formulate this structure as group‐label shift (GLS) and pair it with a class‐specific exponential tilting model for the joint density ratio between the target and source populations. The GLS framework generalizes existing shift assumptions by allowing heterogeneity in both feature and label distributions while mitigating spurious cross‐domain correlations. Under sufficient support and variation conditions on the source outcome regression, the tilting parameters are identifiable from the source distribution of covariates and outcomes, together with the target covariate distribution. A computationally efficient two‐step likelihood‐based estimation procedure is developed. We derive consistency and asymptotic normality for the resulting estimators and extend the theory to receiver operating characteristic curves, the area under the curve, and related target functionals, addressing the nonstandard challenges posed by plug‐in classifiers. Simulation studies demonstrate that the proposed method outperforms existing alternatives under GLS settings. An application to the Waterbirds data set further illustrates its effectiveness in transfer learning and classification.
ABSTRACT In this paper, we introduce a novel framework that uses sliced representative points of distribution functions to construct sliced space‐filling designs for mixture components. Using energy distance decomposition, we first establish a relationship between the representativeness of the full point set and its sliced subsets. Based on this, we propose two contrasting construction methods that prioritize representativeness at either the full set or the subset level. To balance both levels, we further develop a hybrid energy distance criterion and corresponding one‐shot and sequential construction algorithms. An accompanying R package is provided for practical use. We also establish the distributional convergence of the point sets and subsets generated by all three methods. Numerical results show that designs based on sliced representative points achieve significant improvements in both space‐filling performance and predictive accuracy.
ABSTRACT Measuring the correlation between two random vectors is required and plays an important role in almost every scientific field and correspondingly many criteria have been proposed in the literature. In this paper, we investigate a new correlation measure and propose an empirical estimator for interval‐censored failure time data. The theoretical guarantee of the new measure and the asymptotic properties of the estimator are established and in particular, the estimator is shown to be consistent and asymptotically normally distributed. One main advantage of the new correlation is that it significantly reduces the computational burden compared to some existing criteria for high‐dimensional data. By using the new measure, a model‐free feature screening procedure is proposed and both sure screening property and rank consistency of the proposed approach are established. An extensive simulation study indicates that the screening procedure works well in practical situations and an illustration is provided.
ABSTRACT We consider the problem of pairwise Kalman filter (PKF) robustness in the context of Gaussian homogeneous Markov pairwise models (GH‐PMMs). We provide a fast and accurate sequential calculation of the mean square error increase for the pairwise Kalman filter when the parameters of the model used deviate from the actual parameters. We illustrate the relevance of the theoretical results by studying filter deterioration in a specific situation, where one replaces the real PMM model by the classical homogeneous Gaussian state‐space model (GH‐SSM). We also present an application to the real‐world problem of estimating soil moisture by filtering the temperature sequence.
