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作者：Niu, By ziang; Chakraborty, Abhinav; Dukes, Oliver; Katsevich, Eugene
作者单位：University of Pennsylvania; Ghent University
摘要：Model-X approaches to testing conditional independence between a predictor and an outcome variable given a vector of covariates usually assume exact knowledge of the conditional distribution of the predictor given the covariates. Nevertheless, model-X methodologies are often deployed with this conditional distribution learned in sample. We investigate the consequences of this choice through the lens of the distilled conditional randomization test (dCRT). We find that Type-I error control is st...
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作者：Chen, YinFeng; Jiao, YuLing; Qiu, Rui; Hu, Zhou
作者单位：East China Normal University; Wuhan University
摘要：Linear sufficient dimension reduction, as exemplified by sliced inverse regression, has seen substantial development in the past thirty years. However, with the advent of more complex scenarios, nonlinear dimension reduction has gained considerable interest recently. This paper introduces a novel method for nonlinear sufficient dimension reduction, utilizing the generalized martingale difference divergence measure in conjunction with deep neural networks. The optimal solution of the proposed o...
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作者：Ding, Yi; Zheng, Xinghua
作者单位：University of Macau; Hong Kong University of Science & Technology
摘要：We study the estimation of high-dimensional covariance matrices and their empirical spectral distributions under dynamic volatility models. Data under such models have nonlinear dependency both cross-sectionally and temporally. We establish the condition under which the limiting spectral distribution (LSD) of the sample covariance matrix under scalar BEKK models is different from the i.i.d. case. We then propose a time-variation adjusted (TV-adj) sample covariance matrix and prove that its LSD...
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作者：Brutsche, Johannes; Rohde, Angelika
作者单位：University of Freiburg
摘要：Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift b to some reference drift b0: At prescribed significance, we simultaneously identify those regions where violation from similarity occurs, without a priori knowledge of their number, size and location. This test is shown to be minimax-optimal and adaptive. At the same time, the procedure is robust under small deviation from Brownian motion as the driving noise process. A detailed ...
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作者：Hagrass, Omar; Sriperumbudur, Bharath K.; Li, Bing
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Over the last decade, an approach that has gained a lot of popularity to mains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of probability distributions. The main goal of our work is to understand the optimality of two-sample tests constructed based on this approach. First, we show the popular MMD (maximum mean discrepancy) twosample test to be not optimal in terms of the separation boundary measured in Hellinger distance. Second, we propose a modification to the...
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作者：Ki, Dohyeong; Fang, Billy; Guntuboyina, Adityanand
作者单位：University of California System; University of California Berkeley; Alphabet Inc.; Google Incorporated
摘要：Multivariate adaptive regression splines (MARS) is a popular method for nonparametric regression introduced by Friedman in 1991. MARS fits simple nonlinear and non-additive functions to regression data. We propose and study a natural lasso variant of the MARS method. Our method is based on least squares estimation over a convex class of functions obtained by considering infinite-dimensional linear combinations of functions in the MARS basis and imposing a variation based complexity constraint....
