{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T15:41:02Z","timestamp":1791301262609,"version":"4.1.0"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2012,5,21]],"date-time":"2012-05-21T00:00:00Z","timestamp":1337558400000},"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":[[2012,10]]},"abstract":"<jats:p>Economic data are frequently generated by stochastic processes that can be modeled as realizations of random functions (functional data). This paper adapts the specification test for functional data developed by Bugni, Hall, Horowitz, and Neumann (2009, <jats:italic>Econometrics Journal<\/jats:italic>12, S1\u2013S18) to the presence of missing observations. By using a worst case scenario approach, our method is able to extract the information available in the observed portion of the data while being agnostic about the nature of the missing observations. The presence of missing data implies that our test will not only result in the rejection or lack of rejection of the null hypothesis, but it may also be inconclusive.<\/jats:p><jats:p>Under the null hypothesis, our specification test will reject the null hypothesis with a probability that, in the limit, does not exceed the significance level of the test. Moreover, the power of the test converges to one whenever the distribution of the observations conveys that the null hypothesis is false.<\/jats:p><jats:p>Monte Carlo evidence shows that the test may produce informative results (either rejection or lack of rejection of the null hypothesis) even under the presence of significant amounts of missing data. The procedure is illustrated by testing whether the Burdett\u2013Mortensen labor market model is the correct framework for wage paths constructed from the National Longitudinal Survery of Youth, 1979 survey.<\/jats:p>","DOI":"10.1017\/s0266466612000023","type":"journal-article","created":{"date-parts":[[2012,5,21]],"date-time":"2012-05-21T09:56:45Z","timestamp":1337594205000},"page":"959-1002","source":"Crossref","is-referenced-by-count":17,"title":["SPECIFICATION TEST FOR MISSING FUNCTIONAL DATA"],"prefix":"10.1017","volume":"28","author":[{"given":"Federico A.","family":"Bugni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2012,5,21]]},"reference":[{"key":"S0266466612000023_ref29","first-page":"299","article-title":"More on confidence intervals for partially identified parameters","volume":"77","author":"Stoye","year":"2009","journal-title":"Econometrica"},{"key":"S0266466612000023_ref28","volume-title":"Real Analysis","author":"Royden","year":"1988"},{"key":"S0266466612000023_ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6598-4"},{"key":"S0266466612000023_ref24","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/7147.001.0001","volume-title":"Wage Dispersion: Why Are Similar Workers Paid Differently?","author":"Mortensen","year":"2003"},{"key":"S0266466612000023_ref21","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/231","author":"Ito","year":"2006","journal-title":"Essentials of Stochastic Processes"},{"key":"S0266466612000023_ref23","volume-title":"Partial Identification of Probability Distributions","author":"Manski","year":"2003"},{"key":"S0266466612000023_ref19","volume-title":"The Theory of Stochastic Processes I","author":"Gihman","year":"1974"},{"key":"S0266466612000023_ref17","first-page":"1","article-title":"Random projections and goodness-of-fit tests in infinite dimensional spaces","volume":"37","author":"Cuesta-Albertos","year":"2006","journal-title":"Bulletin of the Brazilian Mathematical Society"},{"key":"S0266466612000023_ref18","volume-title":"Stochastic Processes","author":"Doob","year":"1990"},{"key":"S0266466612000023_ref13","doi-asserted-by":"publisher","DOI":"10.2307\/2527292"},{"key":"S0266466612000023_ref11","unstructured":"Bugni F.A. , Canay I.A. , & Shi X. (2012) Specification testing in partially identified models defined by moment inequalities. Mimeo, Duke University, Northwestern University, and University of Wisconsin, Madison."},{"key":"S0266466612000023_ref9","doi-asserted-by":"crossref","first-page":"735","DOI":"10.3982\/ECTA8056","article-title":"Bootstrap inference in partially identified models defined by moment inequalities: Coverage of the identified set","volume":"78","author":"Bugni","year":"2010","journal-title":"Econometrica"},{"key":"S0266466612000023_ref8","doi-asserted-by":"publisher","DOI":"10.1111\/1468-2354.00112"},{"key":"S0266466612000023_ref6","unstructured":"Bierens H.J. & Wang L. (2010) Integrated Conditional Moment Test for Parametric Conditional Distribution. Mimeo, Pennsylvania State University."},{"key":"S0266466612000023_ref3","volume-title":"Topics in Stochastic Processes","author":"Ash","year":"1975"},{"key":"S0266466612000023_ref22","doi-asserted-by":"publisher","DOI":"10.2307\/145818"},{"key":"S0266466612000023_ref4","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2008.00859.x"},{"key":"S0266466612000023_ref2","doi-asserted-by":"crossref","first-page":"119","DOI":"10.3982\/ECTA7502","article-title":"Inference for parameters defined by moment inequalities using generalized moment selection","volume":"78","author":"Andrews","year":"2010","journal-title":"Econometrica"},{"key":"S0266466612000023_ref30","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660016503X"},{"key":"S0266466612000023_ref7","volume-title":"Probability and Measure","author":"Billingsley","year":"1995"},{"key":"S0266466612000023_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2008.03.015"},{"key":"S0266466612000023_ref5","unstructured":"Bierens H.J. (2009) Consistent Model Specification Tests. Mimeo, Pennsylvania State University."},{"key":"S0266466612000023_ref1","doi-asserted-by":"publisher","DOI":"10.2307\/2171880"},{"key":"S0266466612000023_ref12","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2008.00266.x"},{"key":"S0266466612000023_ref15","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2007.00794.x"},{"key":"S0266466612000023_ref20","doi-asserted-by":"publisher","DOI":"10.2307\/1912352"},{"key":"S0266466612000023_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.11.009"},{"key":"S0266466612000023_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.08.001"},{"key":"S0266466612000023_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2006.09.007"},{"key":"S0266466612000023_ref10","doi-asserted-by":"crossref","unstructured":"Bugni F.A. (2012) A comparison of inferential methods in partially identified models in terms of error in coverage probability. 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