{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T02:26:26Z","timestamp":1789784786694,"version":"4.0.1"},"reference-count":62,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2011,3,3]],"date-time":"2011-03-03T00:00:00Z","timestamp":1299110400000},"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":[[2011,8]]},"abstract":"<jats:p>A new class of large-sample covariance and spectral density matrix estimators is proposed based on the notion of flat-top kernels. The new estimators are shown to be higher-order accurate when higher-order accuracy is possible. A discussion on kernel choice is presented as well as a supporting finite-sample simulation. The problem of spectral estimation under a potential lack of finite fourth moments is also addressed. The higher-order accuracy of flat-top kernel estimators typically comes at the sacrifice of the positive semidefinite property. Nevertheless, we show how a flat-top estimator can be modified to become positive semidefinite (even strictly positive definite) while maintaining its higher-order accuracy. In addition, an easy (and consistent) procedure for optimal bandwidth choice is given; this procedure estimates the optimal bandwidth associated with each individual element of the target matrix, automatically sensing (and adapting to) the underlying correlation structure.<\/jats:p>","DOI":"10.1017\/s0266466610000484","type":"journal-article","created":{"date-parts":[[2011,3,3]],"date-time":"2011-03-03T09:43:36Z","timestamp":1299145416000},"page":"703-744","source":"Crossref","is-referenced-by-count":87,"title":["HIGHER-ORDER ACCURATE, POSITIVE SEMIDEFINITE ESTIMATION OF LARGE-SAMPLE COVARIANCE AND SPECTRAL DENSITY MATRICES"],"prefix":"10.1017","volume":"27","author":[{"given":"Dimitris N.","family":"Politis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2011,3,3]]},"reference":[{"key":"S0266466610000484_ref50","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1962.10490039"},{"key":"S0266466610000484_ref44","doi-asserted-by":"publisher","DOI":"10.1080\/10485250310001604659"},{"key":"S0266466610000484_ref40","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706962"},{"key":"S0266466610000484_ref49","doi-asserted-by":"publisher","DOI":"10.1081\/ETC-120028836"},{"key":"S0266466610000484_ref53","first-page":"267","volume-title":"Handbook of Statistics","volume":"15","author":"Robinson","year":"1997"},{"key":"S0266466610000484_ref55","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993146"},{"key":"S0266466610000484_ref38","doi-asserted-by":"publisher","DOI":"10.2307\/2297912"},{"key":"S0266466610000484_ref39","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1996.tb00284.x"},{"key":"S0266466610000484_ref45","first-page":"283","article-title":"A heavy-tailed distribution for ARCH residuals with application to volatility prediction","volume":"5","author":"Politis","year":"2004","journal-title":"Annals of Economics and Finance"},{"key":"S0266466610000484_ref31","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3803-2"},{"key":"S0266466610000484_ref57","first-page":"67","article-title":"Lower bound for the risk of spectral density estimates","volume":"13","author":"Samarov","year":"1977","journal-title":"Problems of Informmation Transmission"},{"key":"S0266466610000484_ref30","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466605050565"},{"key":"S0266466610000484_ref29","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00366"},{"key":"S0266466610000484_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.06.004"},{"key":"S0266466610000484_ref37","doi-asserted-by":"publisher","DOI":"10.2307\/1913610"},{"key":"S0266466610000484_ref26","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.2007.00548.x"},{"key":"S0266466610000484_ref46","unstructured":"Politis D.N. 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