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作者：Zhan, Haoran; Zhang, Mingke; Xia, Yingcun
作者单位：National University of Singapore; University of Electronic Science & Technology of China
摘要：Projection pursuit regression (PPR) and artificial neural networks (ANNs), both introduced around the same time, share a similar approach to approximating complex structures in data. However, PPR has received far less attention than ANNs and other popular statistical learning methods such as random forests (RF) and support vector machines (SVM). In this paper, we revisit the estimation of PPR and propose an optimal greedy algorithm and an ensemble approach via feature bagging, hereafter referr...
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作者：Giordano, Matteo; Wang, Sven
作者单位：University of Turin; Humboldt University of Berlin
摘要：We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of the likelihood and its gradient, and computational methods have thus far largely resorted to expensive simulation-based techniques. In this article, we propose a new computational approach which is motivated by PDE theory and is built around the characterisat...
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作者：Ando, Tomohiro; Li, Ker-chau
作者单位：University of Melbourne; University of California System; University of California Los Angeles
摘要：Noncrossing quantile regression with an emphasis on model misspecification is investigated. While many sophisticated methods for noncrossing quantile have been developed under the assumption of correct model specification, model misspecification and extrapolation are two issues rarely considered in the literature. In this paper, a monotonicity representation for quantile regression models is obtained under simplex embedding, which leads to the simplex quantile regression (SQR) method. SQR mode...
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作者：Gao, Zhe; Wang, Roulin; Wang, Xueqin; Zhang, Heping
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; East China Normal University; Yale University
摘要：The exploration of associations between random objects with complex geometric structures has catalyzed the development of various novel statistical tests encompassing distance-based and kernel-based statistics. These methods have various strengths and limitations. One problem is that their test statistics tend to converge to asymptotic null distributions involving secondorder Wiener chaos, which are hard to compute and need approximation or permutation techniques that use much computing power ...
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作者：Kotekal, Subhodh; Gao, Chao
作者单位：University of Chicago
摘要：We study estimation of an s-sparse signal in the p-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely, the rate scales with respect to p-2s and exhibits a phase transition at p-2s asymptotic to root root p root p. Correlation is shown to be a blessing, provided it is sufficiently strong and the critical correlation level exhibits a delicate dependence on the sparsity level. Due to correlation, the ...
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作者：Zhou, Yuchen; Chen, Yuxin
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Pennsylvania
摘要：This paper is concerned with estimating the column subspace of a low- rank matrix X star E Rn1xn2 from contaminated data. How to obtain optimal statistical accuracy while accommodating the widest range of signalto-noise ratios (SNRs) becomes particularly challenging in the presence of heteroskedastic noise and unbalanced dimensionality (i.e., n2 >> n1). While the state-of-the-art algorithm HeteroPCA emerges as a powerful solution for solving this problem, it suffers from the curse of ill-condi...
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作者：Cattaneo, Matias D.; Yu, Ruiqi Rae
作者单位：Princeton University
摘要：This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on d-variate random vectors (d >= 1). First, a uniform Gaussian strong approximation is established for general empirical processes indexed by possibly Lipschitz functions, improving on previous results in the literature. In the setting considered by Rio (Probab. Theory Related Fields 98 (1994) 21-45), and if the function class is Lipschitzian, our result improves the ap...
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作者：Morikawa, Kosuke; Terada, Yoshikazu; Kim, Jae Kwang
作者单位：University of Osaka; RIKEN; Iowa State University
摘要：In probability sampling, sampling weights are often used to remove selection bias in the sample. The Horvitz-Thompson estimator is well known to be consistent and asymptotically normally distributed; however, it is not necessarily efficient. This study derives the semiparametric efficiency bound for various target parameters by considering the survey weights as random variables and consequently proposes two semiparametric estimators with working models on the survey weights. One estimator assu...
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作者：Arias-Castro, Ery; Qiao, Wanli
作者单位：University of California System; University of California San Diego; University of California System; University of California San Diego; George Mason University
摘要：We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for Euclidean data to be applicable to distributional data. We focus on classical scaling and Isomap-prototypical methods that have played important roles in these areas-and showcase their use in the context of distributional data analysis. In the process, we highlight the crucial role that the ambient metric plays.
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作者：Brown, Benjamin; Zhang, Kai; Meng, Xiao-Li
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; Harvard University
摘要：Two linearly uncorrelated binary variables must be also independent because nonlinear dependence cannot manifest with only two possible states. This inherent linearity is the atom of dependency constituting any complex form of relationship. Inspired by this observation, we develop a framework called binary expansion linear effect (BELIEF) for understanding arbitrary relationships with a binary outcome. Models from the BELIEF framework are easily interpretable because they describe the associat...
