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变量缩减后的模型置信集合推断AI 解读

Summary Sparsity in a regression context makes the model itself an object of interest, pointing to a confidence set of models as the appropriate presentation of evidence. A difficulty in areas such as genomics, where the number of candidate variables is vast, arises from the need for preliminary reduction prior to the assessment of models. The present paper considers a resolution using inferential separations fundamental to the Fisherian approach to conditional inference,…

回归图与诱导稀疏性的重参数化AI 解读

Summary That parameterization and sparsity are inherently linked raises the possibility that relevant models, not obviously sparse in their natural formulation, exhibit a population-level sparsity after reparameterization. In covariance models, positive definiteness enforces additional constraints on how sparsity can legitimately manifest. It is therefore natural to consider reparameterization maps in which sparsity respects positive definiteness. This paper provides insight…

分离数据下高维 Logistic 回归模型的推断AI 解读

Summary Direct use of the likelihood function typically produces severely biased estimates when the dimension of the parameter vector is large relative to the effective sample size. With linearly separable data generated from a logistic regression model, the loglikelihood function asymptotes and the maximum likelihood estimator does not exist. We show that an exact analysis for each regression coefficient produces half-infinite confidence sets for some parameters when the…

黎曼流形上空间点过程强度函数的非参数估计AI 解读

Summary This paper is concerned with nonparametric estimation of the intensity function of a point process on a Riemannian manifold. It provides a first-order asymptotic analysis of the proposed kernel estimator for Poisson processes, supplemented by empirical work to probe the behaviour in finite samples and under other generative regimes. The investigation highlights the scope for finite-sample improvements by allowing the bandwidth to adapt to local curvature.

稀疏尺度与协方差矩阵变换AI 解读

Summary We develop a theory of covariance and concentration matrix estimation on any given or estimated sparsity scale when the matrix dimension is larger than the sample size. Nonstandard sparsity scales are justified when such matrices are nuisance parameters, distinct from interest parameters, which should always have a direct subject-matter interpretation. The matrix logarithmic and inverse scales are studied as special cases, with the corollary that a constrained…