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高维生存数据的删失秩独立筛选AI 解读

In modern statistical applications, the dimension of covariates can be much larger than the sample size. In the context of linear models, correlation screening (Fan and Lv, 2008) has been shown to reduce the dimension of such data effectively while achieving the sure screening property, i.e., all of the active variables can be retained with high probability. However, screening based on the Pearson correlation does not perform well when applied to contaminated covariates…

超高维数据中稀疏区段的稳健检测与识别AI 解读

Summary Copy number variants (CNVs) are alternations of DNA of a genome that result in the cell having less or more than two copies of segments of the DNA. CNVs correspond to relatively large regions of the genome, ranging from about one kilobase to several megabases, that are deleted or duplicated. Motivated by CNV analysis based on next generation sequencing data, we consider the problem of detecting and identifying sparse short segments hidden in a long linear sequence of…

异质且异方差混合分布的最优检测AI 解读

Summary The problem of detecting heterogeneous and heteroscedastic Gaussian mixtures is considered. The focus is on how the parameters of heterogeneity, heteroscedasticity and proportion of non-null component influence the difficulty of the problem. We establish an explicit detection boundary which separates the detectable region where the likelihood ratio test is shown to detect the presence of non-null effects reliably from the undetectable region where no method can do…

稀疏信号段的最优识别及其拷贝数变异应用AI 解读

Motivated by DNA copy number variation (CNV) analysis based on high-density single nucleotide polymorphism (SNP) data, we consider the problem of detecting and identifying sparse short segments in a long one-dimensional sequence of data with additive Gaussian white noise, where the number, length and location of the segments are unknown. We present a statistical characterization of the identifiable region of a segment where it is possible to reliably separate the segment…