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A local approach to estimation in discrete loglinear models
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Empirical Likelihood for Linear Structural Equation Models with Dependent Errors
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Conditional Path Analysis in SinglyConnected Path Diagrams
We extend the classical path analysis by showing that, for a singlyconn...
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If You Must Choose Among Your Children, Pick the Right One
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Bahadur Efficiency in Tensor CurieWeiss Models
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Gaussian Graphical Model exploration and selection in high dimension low sample size setting
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The Maximum Likelihood Threshold of a Path Diagram
Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and bidirected edges that indicate possible correlations among noise terms. Using this graphical representation, we determine the maximum likelihood threshold, that is, the minimum sample size at which the likelihood function of a Gaussian structural equation model is almost surely bounded. Our result allows the model to have feedback loops and is based on decomposing the path diagram with respect to the connected components of its bidirected part. We also prove that if the sample size is below the threshold, then the likelihood function is almost surely unbounded. Our work clarifies, in particular, that standard likelihood inference is applicable to sparse highdimensional models even if they feature feedback loops.
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