{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T00:21:53Z","timestamp":1789777313173,"version":"4.0.1"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2007,10,25]],"date-time":"2007-10-25T00:00:00Z","timestamp":1193270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Institute of Health","award":["IR01GM072876:01A1"],"award-info":[{"award-number":["IR01GM072876:01A1"]}]},{"name":"Interuniversity Attraction Pole research networks","award":["P5\/24"],"award-info":[{"award-number":["P5\/24"]}]},{"name":"Interuniversity Attraction Pole research networks","award":["P6\/03"],"award-info":[{"award-number":["P6\/03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007,11,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In the common non-parametric regression model the problem of testing for the parametric form of the conditional variance is considered. A stochastic process based on the difference between the empirical processes that are obtained from the standardized non-parametric residuals under the null hypothesis (of a specific parametric form of the variance function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Kolmogorov\u2013Smirnov and a Cram\u00e9r\u2013von Mises type of statistic for testing the parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2007.00616.x","type":"journal-article","created":{"date-parts":[[2007,10,27]],"date-time":"2007-10-27T17:42:25Z","timestamp":1193506945000},"page":"903-917","source":"Crossref","is-referenced-by-count":69,"title":["A New Test for the Parametric Form of the Variance Function in Non-Parametric Regression"],"prefix":"10.1093","volume":"69","author":[{"given":"Holger","family":"Dette","sequence":"first","affiliation":[{"name":"Ruhr-Universit\u00e4t Bochum , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Natalie","family":"Neumeyer","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Hamburg , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ingrid Van","family":"Keilegom","sequence":"additional","affiliation":[{"name":"Universit\u00e9 catholique de Louvain , Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2007,10,25]]},"reference":[{"key":"2023040707275184800_","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1111\/1467-9469.00254","article-title":"Nonparametric estimation of the residual distribution","volume":"28","author":"Akritas","year":"2001","journal-title":"Scand. 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