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作者：Li, Tianxi; Levina, Elizaveta; Zhu, Ji
作者单位：University of Virginia; University of Michigan System; University of Michigan
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作者：Cannings, Timothy, I; Fan, Yingying; Samworth, Richard J.
作者单位：University of Edinburgh; University of Southern California; University of Cambridge
摘要：We study the effect of imperfect training data labels on the performance of classification methods. In a general setting, where the probability that an observation in the training dataset is mislabelled may depend on both the feature vector and the true label, we bound the excess risk of an arbitrary classifier trained with imperfect labels in terms of its excess risk for predicting a noisy label. This reveals conditions under which a classifier trained with imperfect labels remains consistent...
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作者：Lei, J.; Lin, K. Z.
作者单位：Carnegie Mellon University
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作者：Kong, Xinbing
作者单位：Nanjing Audit University
摘要：We introduce a random-perturbation-based rank estimator of the number of factors of a large-dimensional approximate factor model. An expansion of the rank estimator demonstrates that the random perturbation reduces the biases due to the persistence of the factor series and the dependence between the factor and error series. A central limit theorem for the rank estimator with convergence rate higher than root n gives a new hypothesis-testing procedure for both one-sided and two-sided alternativ...
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作者：Lee, C. E.; Zhang, X.; Shao, X.
作者单位：University of Tennessee System; University of Tennessee Knoxville; Texas A&M University System; Texas A&M University College Station; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We propose a new nonparametric conditional mean independence test for a response variable Y and a predictor variable X where either or both can be function-valued. Our test is built on a new metric, the so-called functional martingale difference divergence, which fully characterizes the conditional mean dependence of Y given X and extends the martingale difference divergence proposed by Shao & Zhang (2014). We define an unbiased estimator of functional martingale difference divergence by using...
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作者：Qiao, Xinghao; Qian, Cheng; James, Gareth M.; Guo, Shaojun
作者单位：University of London; London School Economics & Political Science; University of Southern California; Renmin University of China
摘要：We consider estimating a functional graphical model from multivariate functional observations. In functional data analysis, the classical assumption is that each function has been measured over a densely sampled grid. However, in practice the functions have often been observed, with measurement error, at a relatively small number of points. We propose a class of doubly functional graphical models to capture the evolving conditional dependence relationship among a large number of sparsely or de...
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作者：Gao, Chao; Ma, Zongming
作者单位：University of Chicago; University of Pennsylvania
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作者：Vihola, Matti; Franks, Jordan
作者单位：University of Jyvaskyla
摘要：Approximate Bayesian computation enables inference for complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We propose an approach that involves using a relatively large tolerance for the Markov chain Monte Carlo sampler to ensure sufficient mixing and post-pro...
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作者：Li, Housen; Munk, Axel; Sieling, Hannes; Walther, Guenther
作者单位：University of Gottingen; Stanford University
摘要：The histogram is widely used as a simple, exploratory way of displaying data, but it is usually not clear how to choose the number and size of the bins. We construct a confidence set of distribution functions that optimally deal with the two main tasks of the histogram: estimating probabilities and detecting features such as increases and modes in the distribution. We define the essential histogram as the histogram in the confidence set with the fewest bins. Thus the essential histogram is the...
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作者：Tyler, David E.; Yi, Mengxi
作者单位：Rutgers University System; Rutgers University New Brunswick; University of International Business & Economics
摘要：The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.
