Non-probability samples are widely adopted in surveys for cost and efficiency, yet the absence of inclusion probabilities challenges finite population inference. A typical solution is integrating them with a reference probability sample using auxiliary information, but existing methods usually assume ignorable selection given covariates. In practice, participation often directly depends on the study variable, making selection nonignorable and standard adjustments invalid. This paper presents a unified likelihood-based framework for estimating finite population means under nonignorable non-probability sampling. The approach integrates empirical likelihood, pseudo-likelihood, and parametric modelling of the participation mechanism, and covers two common survey scenarios: (1) a reference sample with both auxiliary and study variables; (2) a reference sample with auxiliary variables only. Within this framework, we propose three estimators for the finite population mean and establish their asymptotic normality under suitable regularity conditions for survey contexts. Simulations confirm that the proposed estimators outperform existing methods in robustness and reliability when the ignorability assumption is violated. An application to the ESPACOV survey demonstrates the practical utility of the methodology.
We introduce a criterion, named the mean L1 -distance (ML1D) criterion, to construct uniform designs in experiments with mixtures. This criterion allows for a flexible number of design points and produces a more uniform pattern within the experimental region, in terms of representative points of the uniform distribution across that region. We further explore the optimal Scheff & eacute;-type simplex-lattice designs under the ML1D criterion and show that a connection exists between uniform mixture designs and optimal Scheff & eacute;-type simplex-lattice designs. An efficient algorithm is proposed to generate uniform designs under the ML1D criterion. Simulations and applications highlight the advantages of the proposed designs, supporting their use for modelling and prediction in mixture experiments. Our method combines model-based and uniform design principles to enable flexible and efficient mixture experiments.
A fundamental concept in information theory is information entropy, which is used to quantify the degree of uncertainty associated with random variables. Building upon this, relative entropy serves as a measure of the discrepancy between two probability distributions and has been widely studied in statistics. The function of relative entropy in the field of parameter estimation has been extensively investigated. This paper extends existing research by deriving minimum mean relative entropy estimators for the parameters of the Gamma, Laplace, and Rayleigh distributions. Furthermore, we introduce the residual mean relative entropy, a novel measure based on mean relative entropy, and apply it to model comparison. To estimate this measure, we employ kernel density estimation and bootstrap methods. Simulation experiments and empirical analysis demonstrate that the proposed residual mean relative entropy provides an effective new criterion for model comparison.
The comparative analysis of single-cell RNA sequencing (scRNA-seq) datasets across various biological conditions, technology platforms and tissue types reveals crucial insights into cellular heterogeneity and tissue architecture. Recent advances in high-resolution technologies have enabled the profiling of gene expression at the single-cell level, yet inherent heterogeneities between platforms and differences in cell type composition make data integration challenging. We present the FIRM R package, which offers a streamlined workflow for the flexible integration of scRNA-seq data using a re-scaling algorithm that accounts for the effects of cell type composition. FIRM achieves accurate mixing of shared cell type identities and superior preservation of the original structure without overcorrection, generating robust integrated datasets for downstream exploration and analysis.
This paper investigates the asymptotic properties of the Kaplan–Meier and hazard estimators for censored survival time data. We conduct this analysis under the assumption of m-widely acceptable (m-WA) dependence, a generalized form of weak correlation. Using the Fuk–Nagaev inequality, we establish strong consistency and strong representation results for these estimators. Our findings show that the rate of strong consistency is near [Formula: see text] and the remainder term in the strong representation is of the same order. These results generalize and extend existing work for other types of dependent data, such as linearly extended negative quadrant-dependent (LENQD) and extended negative dependent (END) sequences, thereby broadening the theoretical foundation for these widely used statistical tools.
