{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T13:11:19Z","timestamp":1762607479065},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T00:00:00Z","timestamp":1557705600000},"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":[[2019,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>This manuscript considers locally best invariant tests for sphericity in heterogeneous panels. A new integral representation for the characteristic function of the test statistic under the null is presented, along with an algorithm for inverting it to obtain the distribution function. A saddlepoint approximation to the null distribution addresses the need to quickly compute approximate $p$-values in empirical work. The approximation shows substantial improvements over the normal approximation when the cross-sectional dimension is small.<\/jats:p>","DOI":"10.1093\/biomet\/asz018","type":"journal-article","created":{"date-parts":[[2019,3,11]],"date-time":"2019-03-11T20:12:26Z","timestamp":1552335146000},"page":"740-747","source":"Crossref","is-referenced-by-count":1,"title":["Testing for individual sphericity in heterogeneous panels"],"prefix":"10.1093","volume":"106","author":[{"given":"Simon A","family":"Broda","sequence":"first","affiliation":[{"name":"Department of Banking and Finance, University of Zurich, Andreasstrasse 15, 8050 Zurich, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,5,13]]},"reference":[{"key":"2019091012190238900_B1","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1111\/1368-423X.t01-1-00096","article-title":"An optimal test against a random walk component in a non-orthogonal unobserved components model","volume":"5","author":"Bailey,","year":"2002","journal-title":"Economet. 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