{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T09:03:22Z","timestamp":1773219802504,"version":"3.50.1"},"reference-count":13,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[1983,9,1]],"date-time":"1983-09-01T00:00:00Z","timestamp":431222400000},"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":[[1983,9,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title>\n               <jats:p>We consider three simple approaches to rounding error in least squares regression. The first treats the rounded data as if they were unrounded, the second adds an adjustment to the diagonal of the covariance matrix of the variables and the third subtracts an adjustment from the diagonal. The third, Sheppard's corrections, can be motivated as maximum likelihood with small rounding error and either (1) joint normal data or (2) normal residuals, \u201cregular\u201d independent variables, and large samples. Although an example and theory suggest that the third approach is usually preferable to the first two, a generally satisfactory attack on rounding error in regression requires the specification of the full distribution of variables, and convenient computational methods for this problem are not currently available.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1983.tb01230.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T06:45:41Z","timestamp":1544165141000},"page":"51-59","source":"Crossref","is-referenced-by-count":33,"title":["Rounding Error in Regression: The Appropriateness of Sheppard's Corrections"],"prefix":"10.1093","volume":"45","author":[{"given":"Arthur P.","family":"Dempster","sequence":"first","affiliation":[{"name":"Harvard University and University of Chicago \u00a0 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Donald B.","family":"Rubin","sequence":"additional","affiliation":[{"name":"Harvard University and University of Chicago \u00a0 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920554424800_rssb01230-cit-0001","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1080\/01621459.1976.10481507","article-title":"The acceptability of regression solutions: Another look at computational accuracy","volume":"71","author":"Beaton","year":"1976","journal-title":"J. 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Inst."},{"key":"2024090920554424800_rssb01230-cit-0005","first-page":"185","article-title":"Effects of rounding on grouping data","volume-title":"Selected Techniques of Statistical Analysis","author":"Eisenhart","year":"1947"},{"key":"2024090920554424800_rssb01230-cit-0006","first-page":"145","article-title":"Correzione dei momenti quando la curva \u00e8 simmetrica","volume":"16","author":"Elderton","year":"1938","journal-title":"Giornale dell' Istituo Italiano degli Attuari"},{"key":"2024090920554424800_rssb01230-cit-0007","first-page":"309","article-title":"On the mathematical foundations of theoretical statistics","volume":"222","author":"Fisher","year":"1922","journal-title":"Phil. Trans. Roy. Soc. A"},{"key":"2024090920554424800_rssb01230-cit-0008","volume-title":"Regression Estimation from Grouped Observations.","author":"Haitovsky","year":"1973"},{"key":"2024090920554424800_rssb01230-cit-0009","volume-title":"The Advanced Theory of Statistics","author":"Kendall","year":"1962"},{"issue":"7","key":"2024090920554424800_rssb01230-cit-0010","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1017\/S0305004100025512","article-title":"Grouping corrections and maximum likelihood equations","volume":"46","author":"Lindley","year":"1950","journal-title":"Proc. Camb. Phil. Soc."},{"key":"2024090920554424800_rssb01230-cit-0011","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1080\/01621459.1967.10500896","article-title":"An appraisal of least squares programs for the electronic computer from the point of view of the user","volume":"62","author":"Longley","year":"1967","journal-title":"J. Amer. Statist. Ass."},{"key":"2024090920554424800_rssb01230-cit-0012","first-page":"353","article-title":"On the calculation of the most probable values of frequency constants for data arranged according to equidistant divisions of a scale","volume":"29","author":"Sheppard","year":"1898","journal-title":"Proc. London Math. Soc."},{"key":"2024090920554424800_rssb01230-cit-0013","first-page":"248","article-title":"Sheppard's corrections formulae in several variables","volume":"17","author":"Wold","year":"1934","journal-title":"Skand. Aktuartidskr."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1983.tb01230.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/45\/1\/51\/49098094\/jrsssb_45_1_51.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/45\/1\/51\/49098094\/jrsssb_45_1_51.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T21:50:47Z","timestamp":1725918647000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/45\/1\/51\/7027810"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,9,1]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1983,9,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1983.tb01230.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1983,9]]},"published":{"date-parts":[[1983,9,1]]}}}