MSC Codes 60C05, 60J10It is known that for the 2n-step symmetric simple random walk on , two events have the same probability if and only if their sets of paths have the same cardinality. In this article, we construct...
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This paper investigates the connection between neural networks and sufficient dimension reduction (SDR), demonstrating that neural networks inherently perform SDR in regression tasks under appropriate rank regularizat...
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In this paper, we systematically summarize and enhance the understanding of weak convergence and functional limits of record numbers in discrete-time random walks under Spitzer's condition, and extend these findin...
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We thank the editor,Professor Jun Shao,for orga-nizing this stimulating *** are grateful to all discussants for their insightful comments on our review article on the distributed statistical *** to the urgent need to ...
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We thank the editor,Professor Jun Shao,for orga-nizing this stimulating *** are grateful to all discussants for their insightful comments on our review article on the distributed statistical *** to the urgent need to process the datasets with massive sizes,various distributed computing methods have been proposed for the large-scale statistical ***,some important theoretical results were *** we want to give a relatively comprehensive overview on this hot topic,there are still some important works that have been missed in our review written over a year ***,we are glad to see the discussants provide reviews of some new works and *** hope that these discussions and our review would serve as a stimulus for further studies in this rapidly developing area.
We define a model for the joint distribution of multiple continuous latent variables which includes a model for how their correlations depend on explanatory variables. This is motivated by and applied to social scient...
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Multi-regional clinical trial (MRCT) has been common practice for drug development and global registration. The FDA guidance "Demonstrating Substantial Evidence of Effectiveness for Human Drug and Biological Prod...
The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non–nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large an...
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ℓ1-penalized quantile regression (ℓ1-QR) is a useful tool for modeling the relationship between input and output variables when detecting heterogeneous effects in the high-dimensional setting. Hypothesis tests can the...
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ℓ1-penalized quantile regression (ℓ1-QR) is a useful tool for modeling the relationship between input and output variables when detecting heterogeneous effects in the high-dimensional setting. Hypothesis tests can then be formulated based on the debiased ℓ1-QR estimator that reduces the bias induced by Lasso penalty. However, the nonsmoothness of the quantile loss brings great challenges to the computation, especially when the data dimension is high. Recently, the convolution-type smoothed quantile regression (SQR) model has been proposed to overcome such shortcoming, and people developed theory of estimation and variable selection therein. In this work, we combine the debiased method with SQR model and come up with the debiased ℓ1-SQR estimator, based on which we then establish confidence intervals and hypothesis testing in the high-dimensional setup. Theoretically, we provide the non-asymptotic Bahadur representation for our proposed estimator and also the Berry-Esseen bound, which implies the empirical coverage rates for the studentized confidence intervals. Furthermore, we build up the theory of hypothesis testing on both a single variable and a group of variables. Finally, we exhibit extensive numerical experiments on both simulated and real data to demonstrate the good performance of our method.
We report a search for a lepton-portal dark matter model, where dark matter couples to a charged lepton in the standard model. This simplified model naturally leads to photon-mediated dark matter interactions with nuc...
In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficie...
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