Multimodality of the likelihood in the bivariate seemingly unrelated regressions model

By Mathias Drton, Thomas S. Richardson. 2004

80 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/26b7bd228382afba6ddca60809b0cf3a11e92b1a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Mathias Drton
2. Nanny Wermuth
3. Kayvan Sadeghi
4. Thomas S. Richardson
5. Peter Spirtes
6. Marloes H. Maathuis
7. R. Ali
8. Bernd Sturmfels

In Statistics and Probability

1. Mathias Drton
2. Nanny Wermuth
3. Kayvan Sadeghi
4. Bernd Sturmfels
5. Thomas S. Richardson
6. Caroline Uhler
7. Amit Khetan
8. F. Catanese

Citations in the corpus

• Sequences of regressions and their independences (2011, background): “For small sample sizes, a given solution of the likelihood equations of a Gaussian SUR model may not be unique; see Drton and Richardson (2004), Sundberg (2010), while for exclusively discrete variables this will never happen; see Drton (2009).”
• Maximum likelihood estimation for linear Gaussian covariance models (2014, background): “…in maximum likelihood estimation of correlation matrices for Gaussian populations [RM94, SWY00, SO91] or covariance matrices with prescribed zeros [DR04, CDR07], applications of stationary stochastic processes from repeated time series data [And70, And73], Brownian motion tree models for…”
• Identification and Likelihood Inference for Recursive Linear Models with Correlated Errors (2006, unknown): “(S7) In very small samples, or under misspecification, the likelihood function may be multimodal [14] [17].”
• Multivariate Statistical Analysis (2011, background): “…solution for the Gaussian distribution in four variables, split into a response vector Ya and vector variable Yb, was given and an example of a poorly fitting data set with very few observations for which the likelihood equations have two real roots; see Drton and Richardson (2004).”
• Algebraic problems in structural equation modeling (2016, methodology): “We exemplify this for a model discussed in detail in [19].”
• MARKOV EQUIVALENCE FOR ANCESTRAL GRAPHS (2009, background): “In general, there are no closed form expressions for the MLEs for SUR models, iterative fitting methods are required and there may be multiple solutions to the likelihood equations (see [8]).”
• The maximum likelihood degree (2004, methodology): “The notion of ML degree also makes sense for certain parametrized models for continuous data: Drton and Richardson [11] showed that the ML degree of a Gaussian graphical model equals 5, and Bout and Richards [5] studied the ML degree of certain mixture models.”