期刊
ANNALS OF STATISTICS
卷 42, 期 6, 页码 2526-2556出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/14-AOS1260
关键词
Graphical modeling; intervention calculus; nonparametric regression; regularized estimation; sparsity; structural equation model
资金
- People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7) under REA Grant [326496]
- Swiss National Science Foundation [20PA20E-134493]
- Swiss National Science Foundation (SNF) [20PA20E-134493] Funding Source: Swiss National Science Foundation (SNF)
We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding the causal structure. We show that the former can be done with nonregularized (restricted) maximum likelihood estimation while the latter can be efficiently addressed using sparse regression techniques. Thus, we substantially simplify the problem of structure search and estimation for an important class of causal models. We establish consistency of the (restricted) maximum likelihood estimator for low- and high-dimensional scenarios, and we also allow for misspecification of the error distribution: Furthermore, we develop an efficient computational algorithm which can deal with many variables, and the new method's accuracy and performance is illustrated on simulated and real data.
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