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作者：Rinaldo, Alessandro; Wasserman, Larry; G'Sell, Max
作者单位：Carnegie Mellon University
摘要：Several new methods have been recently proposed for performing valid inference after model selection. An older method is sample splitting: use part of the data for model selection and the rest for inference. In this paper, we revisit sample splitting combined with the bootstrap (or the Normal approximation). We show that this leads to a simple, assumption-lean approach to inference and we establish results on the accuracy of the method. In fact, we find new bounds on the accuracy of the bootst...
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作者：Alquier, Pierre; Cottet, Vincent; Lecue, Guillaume
作者单位：Universite Paris Saclay; Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; ENSAE Paris
摘要：We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form (f ) over cap is an element of argmin(f is an element of F) (1/N Sigma(N )(i=1)l(f) (X-i, Y-i) + lambda parallel to f parallel to) when parallel to . parallel to is any norm, F is a convex class of functions and l is a Lipschitz loss function satisfying a Bernstein condition over F. We explore both the bounded and sub-Gaussian stochastic frameworks for the distribution of the f (X-i)'s, wit...
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作者：Chen, Xi; Liu, Weidong; Zhang, Yichen
作者单位：New York University; Shanghai Jiao Tong University; Shanghai Jiao Tong University
摘要：This paper studies the inference problem in quantile regression (QR) for a large sample size n but under a limited memory constraint, where the memory can only store a small batch of data of size m. A natural method is the naive divide-and-conquer approach, which splits data into batches of size m, computes the local QR estimator for each batch and then aggregates the estimators via averaging. However, this method only works when n = o(m(2)) and is computationally expensive. This paper propose...
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作者：Tan, Falong; Zhu, Lixing
作者单位：Hunan University; Beijing Normal University; Hong Kong Baptist University
摘要：In this paper, we construct an adaptive-to-model residual-marked empirical process as the base of constructing a goodness-of-fit test for parametric single-index models with diverging number of predictors. To study the relevant asymptotic properties, we first investigate, under the null and alternative hypothesis, the estimation consistency and asymptotically linear representation of the nonlinear least squares estimator for the parameters of interest and then the convergence of the empirical ...
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作者：Volgushev, Stanislav; Chao, Shih-Kang; Cheng, Guang
作者单位：University of Toronto; Purdue University System; Purdue University
摘要：The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, we propose a two-step procedure: (i) estimate conditional quantile functions at different levels in a parallel computing environment; (ii) construct a conditional quantile regression process through projection based on these estimated quantile curves. Our ...
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作者：Chang, Ming-Chung; Cheng, Shao-Wei; Cheng, Ching-Shui
作者单位：National Central University; National Tsing Hua University; Academia Sinica - Taiwan; University of California System; University of California Berkeley
摘要：Signal aliasing is an inevitable consequence of using fractional factorial designs. Unlike linear models with fixed factorial effects, for Gaussian random field models advocated in some Bayesian design and computer experiment literature, the issue of signal aliasing has not received comparable attention. In the present article, this issue is tackled for experiments with qualitative factors. The signals in a Gaussian random field can be characterized by the random effects identified from the co...
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作者：Drton, Mathias; Fox, Christopher; Wang, Y. Samuel
作者单位：University of Washington; University of Washington Seattle; University of Chicago
摘要：Software for computation of maximum likelihood estimates in linear structural equation models typically employs general techniques from nonlinear optimization, such as quasi-Newton methods. In practice, careful tuning of initial values is often required to avoid convergence issues. As an alternative approach, we propose a block-coordinate descent method that cycles through the considered variables, updating only the parameters related to a given variable in each step. We show that the resultin...
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作者：Schoen, Eric D.; Eendebak, Pieter T.; Goos, Peter
作者单位：KU Leuven; Netherlands Organization Applied Science Research; University of Antwerp
摘要：A conference design is a rectangular matrix with orthogonal columns, one zero in each column, at most one zero in each row and -1's and +1's elsewhere. A definitive screening design can be constructed by folding over a conference design and adding a row vector of zeroes. We prove that, for a given even number of rows, there is just one isomorphism class for conference designs with two or three columns. Next, we derive all isomorphism classes for conference designs with four columns. Based on o...
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作者：Neykov, Matey; Liu, Han
作者单位：Carnegie Mellon University; Northwestern University
摘要：This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property testing is more fundamental than graph recovery, any necessary conditions for property testing imply corresponding conditions for graph recovery, while custom property tests can...
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作者：Zhou, Bo; van den Akker, Ramon; Werker, Bas J. M.
作者单位：Hong Kong University of Science & Technology; Tilburg University; Tilburg University
摘要：We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, that is, have the correct (asymptotic) size, irrespective of the true ...
