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作者：Tibshirani, Ryan J.; Rinaldo, Alessandro; Tibshirani, Rob; Wasserman, Larry
作者单位：Carnegie Mellon University; Carnegie Mellon University; Stanford University
摘要：Recently, Tibshirani et al. [J. Amer. Statist. Assoc. 111 (2016) 600-620] proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this method, without assuming normality. We prove that the test statistic of Tibshirani et al. (2016) is asymptotically valid, as the number of samples n grows and the dimension d of the regression problem stays fixed. Our asym...
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作者：Shi, Chengchun; Fan, Ailin; Song, Rui; Lu, Wenbin
作者单位：North Carolina State University
摘要：Precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information. For many complex diseases, such as cancer, treatment decisions need to be tailored over time according to patients' responses to previous treatments. Such an adaptive strategy is referred as a dynamic treatment regime. A major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of prognostic factors, such...
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作者：Gao, Fuqing; Xiong, Jie; Zhao, Xingqiu
作者单位：Wuhan University; University of Macau; Hong Kong Polytechnic University
摘要：This paper considers self-normalized limits and moderate deviations of nonparametric maximum likelihood estimators for monotone functions. We obtain their self-normalized Cramer-type moderate deviations and limit distribution theorems for the nonparametric maximum likelihood estimator in the current status model and the Grenander-type estimator. As applications of the results, we present a new procedure to construct asymptotical confidence intervals and asymptotical rejection regions of hypoth...
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作者：Wu, Weichi; Zhou, Zhou
作者单位：University of London; University College London; University of Toronto
摘要：We consider structural change testing for a wide class of time series M-estimation with nonstationary predictors and errors. Flexible predictor-error relationships, including exogenous, state-heteroscedastic and autoregressive regressions and their mixtures, are allowed. New uniform Bahadur representations are established with nearly optimal approximation rates. A CUSUMtype test statistic based on the gradient vectors of the regression is considered. In this paper, a simple bootstrap method is...
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作者：Lounici, Karim; Meziani, Katia; Peyre, Gabriel
作者单位：University System of Georgia; Georgia Institute of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Cote d'Azur; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite PSL
摘要：In quantum optics, the quantum state of a light beam is represented through the Wigner function, a density on R-2, which may take negative values but must respect intrinsic positivity constraints imposed by quantum physics. In the framework of noisy quantum homodyne tomography with efficiency parameter 1/2 < eta <= 1, we study the theoretical performance of a kernel estimator of the Wigner function. We prove that it is minimax efficient, up to a logarithmic factor in the sample size, for the L...
