{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T07:07:55Z","timestamp":1781852875030,"version":"3.54.5"},"reference-count":54,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T00:00:00Z","timestamp":1622764800000},"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":[[2022,6]]},"abstract":"<jats:p>We develop the first nonparametric significance test for regression models with classical measurement error in the regressors. In particular, a Cram\u00e9r-von Mises test and a Kolmogorov\u2013Smirnov test for the null hypothesis \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000220_inline1.png\"\/><jats:tex-math>\n$E\\left [Y|X^{*},Z^{*}\\right ]=E\\left [Y|X^{*}\\right ]$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> are proposed when only noisy measurements of \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000220_inline2.png\"\/><jats:tex-math>\n$X^{*}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000220_inline3.png\"\/><jats:tex-math>\n$Z^{*}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> are available. The asymptotic null distributions of the test statistics are derived, and a bootstrap method is implemented to obtain the critical values. Despite the test statistics being constructed using deconvolution estimators, we show that the test can detect a sequence of local alternatives converging to the null at the \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000220_inline4.png\"\/><jats:tex-math>\n$\\sqrt {n}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-rate. We also highlight the finite sample performance of the test through a Monte Carlo study.<\/jats:p>","DOI":"10.1017\/s0266466621000220","type":"journal-article","created":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T09:07:34Z","timestamp":1622797654000},"page":"454-496","source":"Crossref","is-referenced-by-count":1,"title":["NONPARAMETRIC SIGNIFICANCE TESTING IN MEASUREMENT ERROR 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