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Theory"],"published-print":{"date-parts":[[2008,12]]},"abstract":"<jats:p>This paper considers a series estimator of<jats:bold>E<\/jats:bold>[\u03b1(<jats:italic>Y<\/jats:italic>)|\u03bb(<jats:italic>X<\/jats:italic>) = \u03bb\u0304], (\u03b1,\u03bb) \u2208 \ud835\udee2 \u00d7 \u039b, indexed by function spaces, and establishes the estimator's uniform convergence rate over \u03bb\u0304 \u2208<jats:bold>R<\/jats:bold>, \u03b1 \u2208 \ud835\udee2, and \u03bb \u2208 \u039b, when \ud835\udee2 and \u039b have a finite integral bracketing entropy. The rate of convergence depends on the bracketing entropies of \ud835\udee2 and \u039b in general. In particular, we demonstrate that when each \u03bb \u2208 \u039b is locally uniformly \u2112<jats:sub>2<\/jats:sub>-continuous in a parameter from a space of polynomial discrimination and the basis function vector<jats:italic>p<\/jats:italic><jats:sup><jats:italic>K<\/jats:italic><\/jats:sup>in the series estimator keeps the smallest eigenvalue of<jats:bold>E<\/jats:bold>[<jats:italic>p<\/jats:italic><jats:sup><jats:italic>K<\/jats:italic><\/jats:sup>(\u03bb(<jats:italic>X<\/jats:italic>))<jats:italic>p<\/jats:italic><jats:sup><jats:italic>K<\/jats:italic><\/jats:sup>(\u03bb(<jats:italic>X<\/jats:italic>))\u203c] above zero uniformly over \u03bb \u2208 \u039b, we can obtain the same convergence rate as that established by de Jong (2002,<jats:italic>Journal of Econometrics<\/jats:italic>111, 1\u20139).<\/jats:p>","DOI":"10.1017\/s0266466608080584","type":"journal-article","created":{"date-parts":[[2008,7,9]],"date-time":"2008-07-09T08:34:13Z","timestamp":1215592453000},"page":"1463-1499","source":"Crossref","is-referenced-by-count":15,"title":["UNIFORM CONVERGENCE OF SERIES ESTIMATORS OVER FUNCTION SPACES"],"prefix":"10.1017","volume":"24","author":[{"given":"Kyungchul","family":"Song","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,7,9]]},"reference":[{"key":"S0266466608080584_ref031","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993295"},{"key":"S0266466608080584_ref026","unstructured":"Pollard D. 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