High-dimensional covariance matrix estimation plays a central role in multivariate statistical analysis. It is well-known that the sample covariance matrix is singular when the sample size is smaller than the dimension of the variable, but the covariance estimate must be positive-definite. This motivates some modifications of the sample covariance matrix to preserve its efficient estimation of pairwise covariance. In this paper, we modify the sample correlation matrix using the Bagging technique. The proposed Bagging estimator is flexible for general continuous data. Under some mild conditions, we show theoretically that the Bagging estimator can ensure positive-definiteness with probability one in finite samples. We also prove the consistency of the bootstrap estimator of Pearson correlation and the consistency of our Bagging estimator when the dimension p is fixed. Simulation results and a real application are provided to demonstrate that our method strikes a better balance between RMSE and likelihood, and is more robust, than other existing estimators.

CITE-seq provides a powerful method for simultaneously measuring RNA and protein expression at the single-cell level. The integrated analysis of RNA and protein expression in identical cells is crucial for revealing cellular heterogeneity. However, the high experimental costs associated with CITE-seq limit its widespread application. In this paper, we propose scTEL, a deep learning framework based on Transformer encoder layers, to establish a mapping from sequenced RNA expression to unobserved protein expression in the same cells. This computation-based approach significantly reduces the experimental costs of protein expression sequencing. We are now able to predict protein expression using single-cell RNA sequencing (scRNA-seq) data, which is well-established and available at a lower cost. Moreover, our scTEL model offers a unified framework for integrating multiple CITE-seq datasets, addressing the challenge posed by the partial overlap of protein panels across different datasets. Empirical validation on public CITE-seq datasets demonstrates scTEL significantly outperforms existing methods.

With the development of e-commerce industry, the express enterprises are growing up rapidly. At the same time, they produce a large amount of express packaging garbage. The recycling of express packages has become an important issue for environment protection. In this paper, three types of possible policies are discussed for consideration: subsidy, penalty, and tax reduction. We analyze the efficiency of each policy and find the conditions under which the express packaging manufacturers prefer to recycle and reprocess the used products. A two-stage model is established from the perspective of manufacturers to discuss the production and recycling strategies under the three policies. Besides, we suggest an optimal choice between subsidy and tax reduction for the government when the budget is fixed. This paper provides guidelines for the government to improve related policies on promoting the recycling of express packages.

Background: For detecting genotype-phenotype association from case–control single nucleotide polymorphism (SNP) data, one class of methods relies on testing each genomic variant site individually. However, this approach ignores the tendency for associated variant sites to be spatially clustered instead of uniformly distributed along the genome. Therefore, a more recent class of methods looks for blocks of influential variant sites. Unfortunately, existing such methods either assume prior knowledge of the blocks, or rely on ad hoc moving windows. A principled method is needed to automatically detect genomic variant blocks which are associated with the phenotype.Results: In this paper, we introduce an automatic block-wise Genome-Wide Association Study (GWAS) method based on Hidden Markov model. Using case–control SNP data as input, our method detects the number of blocks associated with the phenotype and the locations of the blocks. Correspondingly, the minor allele of each variate site will be classified as having negative influence, no influence or positive influence on the phenotype. We evaluated our method using both datasets simulated from our model and datasets from a block model different from ours, and compared the performance with other methods. These included both simple methods based on the Fisher’s exact test, applied site-by-site, as well as more complex methods built into the recent Zoom-Focus Algorithm. Across all simulations, our method consistently outperformed the comparisons.Conclusions: With its demonstrated better performance, we expect our algorithm for detecting influential variant sites may help find more accurate signals across a wide range of case–control GWAS.

Online reviews are an important part of product information and have important effects on consumers’ purchasing decisions. Some sellers try to manipulate the market by inducing online reviews. In this study, a signal game model based on Bayesian conditional probability is constructed to analyze the preconditions, decision-making process, and effect on market demand and profit of this behavior. The results show that first, when consumer sensitivity to rebates reaches a certain threshold, low-quality sellers will adopt a conditional rebate strategy to induce consumers to give positive reviews. Second, the optimal rebate cost (${\beta }^{*}$) is obtained, where ${\beta }^{*}$ increases with the product price (p), but it is not necessarily monotonic in consumers’ sensitivity to rebates ($\rho$) or the proportion of high-quality products ($\alpha$). Third, the conditional rebate strategy can only work in a market dominated by low-quality goods. Using the conditional rebate strategy in a market dominated by high-quality goods will not bring benefits to low-quality sellers but will harm their profits. This study proposes that some developing online markets have collusive behaviors owing to a lack of regulations and laws, as well as consumers’ concern for small interests. Ensuring the orderly development of online markets will require joint efforts by platform enterprises, government agencies, and consumers.