The maximum likelihood threshold of a path diagram

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

The maximum likelihood threshold of a path diagram. / Drton, Mathias; Fox, Christopher; Kaeufl, Andreas; Pouliot, Guillaume.

I: Annals of Statistics, Bind 47, Nr. 3, 06.2019, s. 1536-1553.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Drton, M, Fox, C, Kaeufl, A & Pouliot, G 2019, 'The maximum likelihood threshold of a path diagram', Annals of Statistics, bind 47, nr. 3, s. 1536-1553. https://doi.org/10.1214/18-AOS1724

APA

Drton, M., Fox, C., Kaeufl, A., & Pouliot, G. (2019). The maximum likelihood threshold of a path diagram. Annals of Statistics, 47(3), 1536-1553. https://doi.org/10.1214/18-AOS1724

Vancouver

Drton M, Fox C, Kaeufl A, Pouliot G. The maximum likelihood threshold of a path diagram. Annals of Statistics. 2019 jun.;47(3):1536-1553. https://doi.org/10.1214/18-AOS1724

Author

Drton, Mathias ; Fox, Christopher ; Kaeufl, Andreas ; Pouliot, Guillaume. / The maximum likelihood threshold of a path diagram. I: Annals of Statistics. 2019 ; Bind 47, Nr. 3. s. 1536-1553.

Bibtex

@article{1617f22ca9224503a151a2027d97453b,
title = "The maximum likelihood threshold of a path diagram",
abstract = "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 high-dimensional models even if they feature feedback loops.",
keywords = "Covariance matrix, graphical model, maximum likelihood, normal distribution, path diagram, structural equation model",
author = "Mathias Drton and Christopher Fox and Andreas Kaeufl and Guillaume Pouliot",
year = "2019",
month = jun,
doi = "10.1214/18-AOS1724",
language = "English",
volume = "47",
pages = "1536--1553",
journal = "Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "3",

}

RIS

TY - JOUR

T1 - The maximum likelihood threshold of a path diagram

AU - Drton, Mathias

AU - Fox, Christopher

AU - Kaeufl, Andreas

AU - Pouliot, Guillaume

PY - 2019/6

Y1 - 2019/6

N2 - 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 high-dimensional models even if they feature feedback loops.

AB - 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 high-dimensional models even if they feature feedback loops.

KW - Covariance matrix

KW - graphical model

KW - maximum likelihood

KW - normal distribution

KW - path diagram

KW - structural equation model

U2 - 10.1214/18-AOS1724

DO - 10.1214/18-AOS1724

M3 - Journal article

VL - 47

SP - 1536

EP - 1553

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 3

ER -

ID: 242777651