{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T11:10:12Z","timestamp":1722856212350},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T00:00:00Z","timestamp":1595376000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,12,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are nonnested, and their intersection is a union of two marginal independences. We consider two sequences of such models, one from each type of independence, that are closest to each other in the Kullback\u2013Leibler sense as they approach the intersection. They become indistinguishable if the signal strength, as measured by the product of two correlation parameters, decreases faster than the standard parametric rate. Under local alternatives at such a rate, we show that the asymptotic distribution of the likelihood ratio depends on where and how the local alternatives approach the intersection. To deal with this nonuniformity, we study a class of envelope distributions by taking pointwise suprema over asymptotic cumulative distribution functions. We show that these envelope distributions are well behaved and lead to model selection procedures with rate-free uniform error guarantees and near-optimal power. To control the error even when the two models are indistinguishable, rather than insist on a dichotomous choice, the proposed procedure will choose either or both models.<\/jats:p>","DOI":"10.1093\/biomet\/asaa040","type":"journal-article","created":{"date-parts":[[2020,5,6]],"date-time":"2020-05-06T11:20:48Z","timestamp":1588764048000},"page":"771-790","source":"Crossref","is-referenced-by-count":1,"title":["On testing marginal versus conditional independence"],"prefix":"10.1093","volume":"107","author":[{"given":"F Richard","family":"Guo","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Washington, Box 354322, Seattle, Washington 98195, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas S","family":"Richardson","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Washington, Box 354322, Seattle, Washington 98195, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,7,22]]},"reference":[{"key":"2020121116434851600_B1","volume-title":"An Introduction to Multivariate Statistical Analysis","author":"Anderson,","year":"1984","edition":"2nd ed"},{"key":"2020121116434851600_B2","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1111\/1468-0262.00210","article-title":"Testing when a parameter is on the boundary of the maintained hypothesis","volume":"69","author":"Andrews,","year":"2001","journal-title":"Econometrica"},{"key":"2020121116434851600_B3","doi-asserted-by":"crossref","DOI":"10.1002\/9781118857281","volume-title":"Information and Exponential Families: In Statistical Theory","author":"Barndorff-Nielsen,","year":"2014"},{"key":"2020121116434851600_B4","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1080\/01621459.1994.10476836","article-title":"$P$ values maximized over a confidence set for the nuisance parameter","volume":"89","author":"Berger,","year":"1994","journal-title":"J. Am. Statist. Assoc."},{"volume-title":"Convex Analysis and Optimization","year":"2003","author":"Bertsekas,","key":"2020121116434851600_B5"},{"key":"2020121116434851600_B6","first-page":"175","article-title":"The use of McKay\u2019s Bessel function curves for graduating frequency distributions","volume":"6","author":"Bhattacharyya,","year":"1942","journal-title":"Sankhy\u0101"},{"volume-title":"The American Occupational Structure","year":"1967","author":"Blau,","key":"2020121116434851600_B7"},{"key":"2020121116434851600_B8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1093\/biomet\/asm007","article-title":"Estimation of a covariance matrix with zeros","volume":"94","author":"Chaudhuri,","year":"2007","journal-title":"Biometrika"},{"key":"2020121116434851600_B9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1979.tb01052.x","article-title":"Conditional independence in statistical theory","volume":"41","author":"Dawid,","year":"1979","journal-title":"J. R. Statist. Soc."},{"key":"2020121116434851600_B10","first-page":"81","volume-title":"Prague Stochastics","author":"Drton,","year":"2006"},{"key":"2020121116434851600_B11","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1214\/07-AOS571","article-title":"Likelihood ratio tests and singularities","volume":"37","author":"Drton,","year":"2009","journal-title":"Ann. Statist."},{"key":"2020121116434851600_B12","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1093\/biomet\/91.3.591","article-title":"Model selection for Gaussian concentration graphs","volume":"91","author":"Drton,","year":"2004","journal-title":"Biometrika"},{"key":"2020121116434851600_B13","first-page":"1273","article-title":"Algebraic statistical models","volume":"17","author":"Drton,","year":"2007","journal-title":"Statist. Sinica"},{"key":"2020121116434851600_B14","doi-asserted-by":"crossref","DOI":"10.1214\/19-AOS1940","article-title":"Model selection and local geometry","author":"Evans,","year":"2020","journal-title":"Ann. Statist. to appear"},{"key":"2020121116434851600_B15","first-page":"329","article-title":"The distribution of the partial correlation coefficient","volume":"3","author":"Fisher,","year":"1924","journal-title":"Metron"},{"key":"2020121116434851600_B16","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1214\/aos\/1176325768","article-title":"On the asymptotics of constrained $ m $-estimation","volume":"22","author":"Geyer,","year":"1994","journal-title":"Ann. Statist."},{"key":"2020121116434851600_B17","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1111\/j.2517-6161.1953.tb00135.x","article-title":"New light on the correlation coefficient and its transforms","volume":"15","author":"Hotelling,","year":"1953","journal-title":"J. R. Statist. Soc."},{"volume-title":"Continuous Univariate Distributions","year":"1995","author":"Johnson,","key":"2020121116434851600_B18"},{"volume-title":"Probabilistic Graphical Models: Principles and Techniques","year":"2009","author":"Koller,","key":"2020121116434851600_B19"},{"key":"2020121116434851600_B20","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522195.001.0001","volume-title":"Graphical Models","author":"Lauritzen,","year":"1996"},{"volume-title":"Testing Statistical Hypotheses","year":"2006","author":"Lehmann,","key":"2020121116434851600_B21"},{"key":"2020121116434851600_B22","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1093\/biomet\/asu038","article-title":"Classification with confidence","volume":"101","author":"Lei,","year":"2014","journal-title":"Biometrika"},{"key":"2020121116434851600_B23","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1214\/ss\/1009212517","article-title":"The emperor\u2019s new tests","volume":"14","author":"Perlman,","year":"1999","journal-title":"Statist. Sci."},{"key":"2020121116434851600_B24","doi-asserted-by":"crossref","DOI":"10.1063\/1.3059791","volume-title":"The Direction of Time","author":"Reichenbach,","year":"1956"},{"key":"2020121116434851600_B25","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1093\/biomet\/90.3.491","article-title":"Uniform consistency in causal inference","volume":"90","author":"Robins,","year":"2003","journal-title":"Biometrika"},{"key":"2020121116434851600_B26","doi-asserted-by":"crossref","DOI":"10.1214\/19-AOS1857","article-title":"The hardness of conditional independence testing and the generalised covariance measure","author":"Shah,","year":"2020","journal-title":"Ann. Statist"},{"volume-title":"Probability Distributions involving Gaussian Random Variables: A Handbook for Engineers and Scientists","year":"2007","author":"Simon,","key":"2020121116434851600_B27"},{"volume-title":"Causation, Prediction, and Search","year":"2000","author":"Spirtes,","key":"2020121116434851600_B28"},{"key":"2020121116434851600_B29","doi-asserted-by":"crossref","DOI":"10.1007\/b13794","volume-title":"Introduction to Nonparametric Estimation","author":"Tsybakov,","year":"2009"},{"volume-title":"Asymptotic Statistics","year":"2000","author":"van der Vaart,","key":"2020121116434851600_B30"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asaa040\/33557852\/asaa040.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/107\/4\/771\/34865893\/asaa040.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/107\/4\/771\/34865893\/asaa040.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T10:27:42Z","timestamp":1722853662000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/107\/4\/771\/5875781"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,22]]},"references-count":30,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,7,22]]},"published-print":{"date-parts":[[2020,12,1]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asaa040","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"type":"print","value":"0006-3444"},{"type":"electronic","value":"1464-3510"}],"subject":[],"published-other":{"date-parts":[[2020,12]]},"published":{"date-parts":[[2020,7,22]]}}}