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作者：Nickl, Richard; van de Geer, Sara
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The problem of constructing confidence sets in the high-dimensional linear model with n response variables and p parameters, possibly p >= n, is considered. Full honest adaptive inference is possible if the rate of sparse estimation does not exceed n(-1/4), otherwise sparse adaptive confidence sets exist only over strict subsets of the parameter spaces for which sparse estimators exist. Necessary and sufficient conditions for the existence of confidence sets that adapt to a fixed sparsity leve...
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作者：He, Yangbo; Jia, Jinzhu; Yu, Bin
作者单位：Peking University; Peking University; University of California System; University of California Berkeley
摘要：Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with currently known algorithms, sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices. In this paper, we design reversible irreducible Markov cha...
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作者：Hong, Yongmiao; Lee, Yoon-Jin
作者单位：Cornell University; Cornell University; Xiamen University; Xiamen University; Indiana University System; Indiana University Bloomington
摘要：The generalized likelihood ratio (GLR) test proposed by Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] and Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer] is a generally applicable nonparametric inference procedure. In this paper, we show that although it inherits many advantages of the parametric maximum likelihood ratio (LR) test, the GLR test does not have the optimal power property. We propose a generally applicable test based on loss funct...
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作者：Cai, T. Tony; Low, Mark G.; Xia, Yin
作者单位：University of Pennsylvania
摘要：Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in terms of an analytic quantity, the local modulus of continuity. This bound depends not only on the function but also the assumed function class. These benchmarks show that the constructed confidence intervals have near minimum expected length for each indivi...
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作者：Khmaladze, Estate
作者单位：Victoria University Wellington
摘要：The paper proposes one-to-one transformation of the vector of components {Y-in}(i=1)(m) of Pearson's chi-square statistic, Y-in = nu(in)-npi/root np(i,) i = l, ... , m, into another vector {Z(in)}(i=1)(m), which, therefore, contains the same statistical information, but is asymptotically distribution free. Hence any functional/test statistic based on {Z(in)}(i=1)(m) is also asymptotically distribution free. Natural examples of such test statistics are traditional goodness-of-fit statistics fro...
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作者：Francq, Christian; Zakoian, Jean-Michel
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Universite de Lille
摘要：This paper considers the statistical inference of the class of asymmetric power-transformed GARCH(1, 1) models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameter, including the power but without the intercept, when strict stationarity does not hold. Two important issues can be tested in this f...
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作者：Tsao, Min; Wu, Fan
作者单位：University of Victoria
摘要：We extend the empirical likelihood of Owen [Ann. Statist. 18 (1990) 90-120] by partitioning its domain into the collection of its contours and mapping the contours through a continuous sequence of similarity transformations onto the full parameter space. The resulting extended empirical likelihood is a natural generalization of the original empirical likelihood to the full parameter space; it has the same asymptotic properties and identically shaped contours as the original empirical likelihoo...
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作者：Nordman, Daniel J.; Bunzel, Helle; Lahiri, Soumendra N.
作者单位：Iowa State University; Iowa State University; Aarhus University; CREATES; North Carolina State University
摘要：Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage accuracy. As an alternative, this paper proposes a new version of BEL based on a simple, though nonstandard, data-blocking rule which uses a data block of every possible length. Consequently, the method does not involve the usual block selection issues and is al...
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作者：Janzing, Dominik; Balduzzi, David; Grosse-Wentrup, Moritz; Schoelkopf, Bernhard
作者单位：Max Planck Society; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between n variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on one variable changes the distribution of the other n - 1 variables. However, quantifying the causal influence of one variable on another one remains a nontrivial question. Here we propose a set of natural, intuitive postulates that a measure of causal strength...
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作者：Vanderweele, Tyler J.; Shpitser, Ilya
作者单位：Harvard University; Harvard T.H. Chan School of Public Health; Harvard University; Harvard T.H. Chan School of Public Health
摘要：The causal inference literature has provided a clear formal definition of confounding expressed in terms of counterfactual independence. The literature has not, however, come to any consensus on a formal definition of a confounder, as it has given priority to the concept of confounding over that of a confounder. We consider a number of candidate definitions arising from various more informal statements made in the literature. We consider the properties satisfied by each candidate definition, p...
