{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,25]],"date-time":"2024-08-25T02:40:04Z","timestamp":1724553604616},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:00:00Z","timestamp":1614556800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:p>In testing for correlation of the errors in regression models, the power of tests can be very low for strongly correlated errors. This counterintuitive phenomenon has become known as the \u201czero-power trap.\u201d Despite a considerable amount of literature devoted to this problem, mainly focusing on its detection, a convincing solution has not yet been found. In this article, we first discuss theoretical results concerning the occurrence of the zero-power trap phenomenon. Then, we suggest and compare three ways to avoid it. Given an initial test that suffers from the zero-power trap, the method we recommend for practice leads to a modified test whose power converges to<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000062_inline1.png\"\/><jats:tex-math>$1$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>as the correlation gets very strong. Furthermore, the modified test has approximately the same power function as the initial test and thus approximately preserves all of its optimality properties. We also provide some numerical illustrations in the context of testing for network generated correlation.<\/jats:p>","DOI":"10.1017\/s0266466621000062","type":"journal-article","created":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T09:27:11Z","timestamp":1614590831000},"page":"1292-1324","source":"Crossref","is-referenced-by-count":2,"title":["HOW TO AVOID THE ZERO-POWER TRAP IN TESTING FOR CORRELATION"],"prefix":"10.1017","volume":"39","author":[{"given":"David","family":"Preinerstorfer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2021,3,1]]},"reference":[{"key":"S0266466621000062_r4","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.3398303"},{"key":"S0266466621000062_r14","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609090641"},{"key":"S0266466621000062_r10","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90125-D"},{"key":"S0266466621000062_r16","doi-asserted-by":"publisher","DOI":"10.1214\/17-EJS1281"},{"key":"S0266466621000062_r6","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2005.00171.x"},{"key":"S0266466621000062_r17","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466614000899"},{"key":"S0266466621000062_r13","doi-asserted-by":"publisher","DOI":"10.1080\/03610920008832630"},{"key":"S0266466621000062_r3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817"},{"volume-title":"Real and Complex Analysis","year":"1987","author":"Rudin","key":"S0266466621000062_r19"},{"key":"S0266466621000062_r11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-41573-4_4"},{"key":"S0266466621000062_r7","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA15844"},{"key":"S0266466621000062_r2","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA12749"},{"volume-title":"Testing Statistical Hypotheses","year":"2005","author":"Lehmann","key":"S0266466621000062_r12"},{"key":"S0266466621000062_r9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2003.11.008"},{"key":"S0266466621000062_r5","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1111\/j.2517-6161.1985.tb01335.x","article-title":"Locally best invariant tests of the error covariance matrix of the linear regression model","volume":"47","author":"King","year":"1985","journal-title":"Journal of the Royal Statistical Society. 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Series C (Applied Statistics)"},{"key":"S0266466621000062_r20","doi-asserted-by":"publisher","DOI":"10.1515\/9783110850826"},{"key":"S0266466621000062_r21","doi-asserted-by":"publisher","DOI":"10.1080\/03610928908830130"},{"key":"S0266466621000062_r8","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(85)90005-3"},{"key":"S0266466621000062_r15","doi-asserted-by":"publisher","DOI":"10.1080\/07474938.2011.553571"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466621000062","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,25]],"date-time":"2024-08-25T01:33:45Z","timestamp":1724549625000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466621000062\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,1]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["S0266466621000062"],"URL":"https:\/\/doi.org\/10.1017\/s0266466621000062","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"type":"print","value":"0266-4666"},{"type":"electronic","value":"1469-4360"}],"subject":[],"published":{"date-parts":[[2021,3,1]]}}}