{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T14:47:22Z","timestamp":1790174842458,"version":"4.1.0"},"reference-count":56,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2015,5,19]],"date-time":"2015-05-19T00:00:00Z","timestamp":1431993600000},"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":[[2016,10]]},"abstract":"<jats:p>We study the asymptotic covariance function of the sample mean and quantile, and derive a new and surprising characterization of the normal distribution: the asymptotic covariance between the sample mean and quantile is constant across all quantiles,<jats:italic>if and only if<\/jats:italic>the underlying distribution is normal. This is a powerful result and facilitates statistical inference. Utilizing this result, we develop a new omnibus test for normality based on the quantile-mean covariance process. Compared to existing normality tests, the proposed testing procedure has several important attractive features. Monte Carlo evidence shows that the proposed test possesses good finite sample properties. In addition to the formal test, we suggest a graphical procedure that is easy to implement and visualize in practice. Finally, we illustrate the use of the suggested techniques with an application to stock return datasets.<\/jats:p>","DOI":"10.1017\/s026646661500016x","type":"journal-article","created":{"date-parts":[[2015,5,19]],"date-time":"2015-05-19T07:15:06Z","timestamp":1432019706000},"page":"1216-1252","source":"Crossref","is-referenced-by-count":23,"title":["A NEW CHARACTERIZATION OF THE NORMAL DISTRIBUTION AND TEST FOR NORMALITY"],"prefix":"10.1017","volume":"32","author":[{"given":"Anil K.","family":"Bera","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antonio F.","family":"Galvao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhijie","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2015,5,19]]},"reference":[{"key":"S026646661500016X_ref29","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/67.1.238"},{"key":"S026646661500016X_ref14","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/70.3.723"},{"key":"S026646661500016X_ref21","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1080\/07350015.1990.10509812","article-title":"Lagrange multiplier tests for normality against semiparametric alternatives","volume":"8","author":"Hall","year":"1990","journal-title":"Journal of Business and Economic Statistics"},{"key":"S026646661500016X_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/1913889"},{"key":"S026646661500016X_ref48","first-page":"439","article-title":"Laplace, Fisher, and the discovery of the concept of sufficiency","volume":"60","author":"Stigler","year":"1973","journal-title":"Biometrika"},{"key":"S026646661500016X_ref41","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbi009"},{"key":"S026646661500016X_ref25","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1080\/07350015.2000.10524846","article-title":"Residual-based tests for normality in autoregressive: Asymptotic theory and simulation evidence","volume":"18","author":"Kilian","year":"2000","journal-title":"Journal of Business and Economic Statistics"},{"key":"S026646661500016X_ref8","doi-asserted-by":"publisher","DOI":"10.1137\/1127098"},{"key":"S026646661500016X_ref52","doi-asserted-by":"publisher","DOI":"10.2307\/1403678"},{"key":"S026646661500016X_ref49","doi-asserted-by":"publisher","DOI":"10.1201\/9780203910894"},{"key":"S026646661500016X_ref34","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1967.10482916"},{"key":"S026646661500016X_ref36","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177731647"},{"key":"S026646661500016X_ref4","first-page":"171","article-title":"A class of distributions which includes the normal ones","volume":"12","author":"Azzalini","year":"1985","journal-title":"Scandinavian Journal of Statistics"},{"key":"S026646661500016X_ref20","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-5957.1990.tb01197.x"},{"key":"S026646661500016X_ref15","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/69.2.391"},{"key":"S026646661500016X_ref53","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1980.10477415"},{"key":"S026646661500016X_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.02.014"},{"key":"S026646661500016X_ref44","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(85)90036-3"},{"key":"S026646661500016X_ref6","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn"},{"key":"S026646661500016X_ref42","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706551"},{"key":"S026646661500016X_ref7","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316962"},{"key":"S026646661500016X_ref46","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/52.3-4.591"},{"key":"S026646661500016X_ref35","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466604204030"},{"key":"S026646661500016X_ref51","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618739"},{"key":"S026646661500016X_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005454"},{"key":"S026646661500016X_ref18","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1930.0185"},{"key":"S026646661500016X_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1765(83)90172-6"},{"key":"S026646661500016X_ref26","doi-asserted-by":"publisher","DOI":"10.2307\/1913643"},{"key":"S026646661500016X_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/2951753"},{"key":"S026646661500016X_ref19","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/34.3-4.209"},{"key":"S026646661500016X_ref27","first-page":"83","article-title":"Sulla determinazione empiricadi una legge di distribuzione","volume":"4","author":"Kolmogorov","year":"1933","journal-title":"Giornale dell\u2019Istituto Italiano degli Attuari"},{"key":"#cr-split#-S026646661500016X_ref33.1","unstructured":"1. 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