## Normal Linear Regression Models with Recursive Graphical Markov Structure (1998)

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Venue: | J. MULTIVARIATE ANAL |

Citations: | 13 - 5 self |

### BibTeX

@ARTICLE{Andersson98normallinear,

author = {Steen A. Andersson and Michael D. Perlman},

title = {Normal Linear Regression Models with Recursive Graphical Markov Structure},

journal = {J. MULTIVARIATE ANAL},

year = {1998},

volume = {66},

pages = {133--187}

}

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### Abstract

A multivariate normal statistical model defined by the Markov pr er deter-- by an acyclic digric admits ar- efactorof its likelihood function (LF) into the pr duct of conditional LFs, eachfactor having the for of a classical multivar - linear rear-- model (# MANOVA model).Her these modelsar extended in anatur way tonor linear rear-- models whose LFs continue to admit suchr- efactor--r frr which maximum likelihoodestimator and likelihoodr (LR) test statistics can beder ed by classical linear methods. The centrdistr -- of the LR test statisticfor testing one such multivariv- norv linear rear model against another isder ed, and there- of theseresesion models to block-r-- enor linear systems is established. It is shown how a collection of nonnested dependentnor linear rear-- models (# seemingly unringly ringly- can be combined into a single multivariv- norvlinear rn grear model by imposing apar-- set of graphical Markov (# conditional independence) restrictions.