{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:06:06Z","timestamp":1785409566570,"version":"3.56.0"},"reference-count":64,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T00:00:00Z","timestamp":1776729600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"abstract":"<jats:p>\n                    We propose a high-dimensional extension of the heteroscedasticity test proposed in Newey and Powell (1987). Our test is based on expectile regression in the proportional asymptotic regime where\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466626100450_inline1.png\"\/>\n                        <jats:tex-math>$n\/p \\to \\delta \\in (0,1]$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . The asymptotic analysis of the test statistic uses the approximate message passing algorithm, from which we obtain the limiting distribution of the test and establish its asymptotic power. The numerical performance of the test is validated through an extensive simulation study. As real-data applications, we present the analysis based on \u201cinternational economic growth\u201d data (Belloni et al., 2013), which is found to be homoscedastic, and \u201csupermarket\u201d data (Lan et al., 2016), which is found to be heteroscedastic.\n                  <\/jats:p>","DOI":"10.1017\/s0266466626100450","type":"journal-article","created":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T07:47:16Z","timestamp":1776757636000},"page":"1-31","source":"Crossref","is-referenced-by-count":1,"title":["HIGH-DIMENSIONAL NEWEY\u2013POWELL TEST VIA APPROXIMATE MESSAGE PASSING"],"prefix":"10.1017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8894-9100","authenticated-orcid":false,"given":"Jing","family":"Zhou","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/027m9bs27","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Manchester"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4798-9904","authenticated-orcid":false,"given":"Hui","family":"Zou","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/017zqws13","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Minnesota"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,4,21]]},"reference":[{"key":"S0266466626100450_r17","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1024691081"},{"key":"S0266466626100450_r39","doi-asserted-by":"publisher","DOI":"10.2307\/1913643"},{"key":"S0266466626100450_r43","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOS1303"},{"key":"S0266466626100450_r32","doi-asserted-by":"publisher","DOI":"10.1017\/S0025557200000711"},{"key":"S0266466626100450_r44","doi-asserted-by":"publisher","DOI":"10.2307\/1911031"},{"key":"S0266466626100450_r12","first-page":"2313","article-title":"The Dantzig selector: Statistical estimation when \n\n\n\n$p$\n\n\n is much larger than \n\n\n\n$n$","volume":"35","author":"Cand\u00e8s","year":"2007","journal-title":"The Annals of Statistics"},{"key":"S0266466626100450_r15","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2011.01652.x"},{"key":"S0266466626100450_r54","doi-asserted-by":"publisher","DOI":"10.1214\/23-AOS2274"},{"key":"S0266466626100450_r10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20192-9"},{"key":"S0266466626100450_r18","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0909892106"},{"key":"S0266466626100450_r31","doi-asserted-by":"publisher","DOI":"10.1214\/22-EJS2092"},{"key":"S0266466626100450_r38","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-economics-063016-103651"},{"key":"S0266466626100450_r57","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS729"},{"key":"S0266466626100450_r19","first-page":"1","volume-title":"2010 IEEE information theory workshop on information theory (ITW 2010, Cairo)","author":"Donoho","year":"2010"},{"key":"S0266466626100450_r50","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1996.tb02080.x"},{"key":"S0266466626100450_r35","doi-asserted-by":"publisher","DOI":"10.1214\/15-EJS1029"},{"key":"S0266466626100450_r45","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2916359"},{"key":"S0266466626100450_r36","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2020.1831924"},{"key":"S0266466626100450_r20","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-015-0675-z"},{"key":"S0266466626100450_r24","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2008.00674.x"},{"key":"S0266466626100450_r4","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2174612"},{"key":"S0266466626100450_r59","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2012.12.009"},{"key":"S0266466626100450_r60","doi-asserted-by":"publisher","DOI":"10.1111\/stan.12274"},{"key":"S0266466626100450_r2","doi-asserted-by":"publisher","DOI":"10.1214\/14-AAP1010"},{"key":"S0266466626100450_r6","doi-asserted-by":"crossref","unstructured":"Belloni, A. , Chernozhukov, V. , & Hansen, C. 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