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作者：Perry, Patrick O.
作者单位：New York University
摘要：Hierarchical models allow for heterogeneous behaviours in a population while simultaneously borrowing estimation strength across all subpopulations. Unfortunately, existing likelihood-based methods for fitting hierarchical models have high computational demands, and these demands have limited their adoption in large-scale prediction and inference problems. The paper proposes a moment-based procedure for estimating the parameters of a hierarchical model which has its roots in a method originall...
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作者：Chen, Kehui; Delicado, Pedro; Muller, Hans-Georg
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; Universitat Politecnica de Catalunya; University of California System; University of California Davis
摘要：We introduce a simple and interpretable model for functional data analysis for situations where the observations at each location are functional rather than scalar. This new approach is based on a tensor product representation of the function-valued process and utilizes eigenfunctions of marginal kernels. The resulting marginal principal components and product principal components are shown to have nice properties. Given a sample of independent realizations of the underlying function-valued st...
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作者：Cai, T. Tony; Sun, Wenguang
作者单位：University of Pennsylvania; University of Southern California
摘要：A common feature in large-scale scientific studies is that signals are sparse and it is desirable to narrow down significantly the focus to a much smaller subset in a sequential manner. We consider two related data screening problems: one is to find the smallest subset such that it virtually contains all signals and another is to find the largest subset such that it essentially contains only signals. These screening problems are closely connected to but distinct from the more conventional sign...
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作者：Passemier, Damien; Li, Zhaoyuan; Yao, Jianfeng
作者单位：University of Hong Kong
摘要：We develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of variables is large in comparison with the sample size. We first unveil the reasons for an observed downward bias of the maximum likelihood estimator of the noise variance when the data dimension is high. We then propose a bias-corrected estimator by using random-matrix theory ...
