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Accordingly, by applying some successful two-sample test statistics in the literature, two tests are constructed to check the lack of fit for low and high dimensional quantile regression models. The low dimensional test works well when the number of covariates is moderate, whereas the high dimensional test can maintain the power when the number of covariates exceeds the sample size. The null distribution of the high dimensional test has an explicit form, and the p-values or critical values can then be calculated directly. The finite sample performance of the tests proposed is examined by simulation studies, and their usefulness is further illustrated by two real examples.<\/jats:p>","DOI":"10.1111\/rssb.12321","type":"journal-article","created":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T00:33:24Z","timestamp":1556584404000},"page":"629-648","source":"Crossref","is-referenced-by-count":17,"title":["Lack-of-Fit Tests for Quantile Regression Models"],"prefix":"10.1093","volume":"81","author":[{"given":"Chen","family":"Dong","sequence":"first","affiliation":[{"name":"Shanghai University of Finance and Economics \u00a0 People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guodong","family":"Li","sequence":"additional","affiliation":[{"name":"University of Hong Kong \u00a0 People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingdong","family":"Feng","sequence":"additional","affiliation":[{"name":"Shanghai University of Finance and Economics \u00a0 People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,4,29]]},"reference":[{"key":"2023022002403549100_","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1214\/aoms\/1177704477","article-title":"On the distribution of the two-sample Cram\u00e9r-von Mises criterion","volume":"33","author":"Anderson","year":"1962","journal-title":"Ann. 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