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作者：Lee, Kuang-Yao; Li, Bing; Zhao, Hongyu
作者单位：Yale University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We propose a non-parametric variable selection method which does not rely on any regression model or predictor distribution. The method is based on a new statistical relationship, called additive conditional independence, that has been introduced recently for graphical models. Unlike most existing variable selection methods, which target the mean of the response, the method proposed targets a set of attributes of the response, such as its mean, variance or entire distribution. In addition, the...
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作者：Guo, Xu; Wang, Tao; Zhu, Lixing
作者单位：Nanjing University of Aeronautics & Astronautics; Hong Kong Baptist University; Yale University; Beijing Normal University
摘要：Local smoothing testing based on multivariate non-parametric regression estimation is one of the main model checking methodologies in the literature. However, the relevant tests suffer from the typical curse of dimensionality, resulting in slow rates of convergence to their limits under the null hypothesis and less deviation from the null hypothesis under alternative hypotheses. This problem prevents tests from maintaining the level of significance well and makes tests less sensitive to altern...
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作者：Bissiri, P. G.; Holmes, C. C.; Walker, S. G.
作者单位：University of Milano-Bicocca; University of Oxford; University of Texas System; University of Texas Austin
摘要：We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such...
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作者：Cholaquidis, Alejandro; Fraiman, Ricardo; Lugosi, Gabor; Pateiro-Lopez, Beatriz
作者单位：Universidad de la Republica, Uruguay; ICREA; Pompeu Fabra University; Universidade de Santiago de Compostela
摘要：We study the problem of estimating a compact set S subset of R-d from a trajectory of a reflected Brownian motion in S with reflections on the boundary of S. We establish consistency and rates of convergence for various estimators of S and its boundary. This problem has relevant applications in ecology in estimating the home range of an animal on the basis of tracking data. There are a variety of studies on the habitat of animals that employ the notion of home range. The paper offers theoretic...
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作者：Peters, Jonas; Buhlmann, Peter; Meinshausen, Nicolai
作者单位：Max Planck Society; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：What is the difference between a prediction that is made with a causal model and that with a non-causal model? Suppose that we intervene on the predictor variables or change the whole environment. The predictions from a causal model will in general work as well under interventions as for observational data. In contrast, predictions from a non-causal model can potentially be very wrong if we actively intervene on variables. Here, we propose to exploit this invariance of a prediction under a cau...
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作者：Guo, Bin; Chen, Song Xi
作者单位：Sichuan University; Peking University; Iowa State University
摘要：We consider testing regression coefficients in high dimensional generalized linear models. By modifying the test statistic of Goeman and his colleagues for large but fixed dimensional settings, we propose a new test, based on an asymptotic analysis, that is applicable for diverging dimensions and is robust to accommodate a wide range of link functions. The power properties of the tests are evaluated asymptotically under two families of alternative hypotheses. In addition, a test in the presenc...
