{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T18:20:50Z","timestamp":1792693250432,"version":"4.5.0"},"reference-count":65,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2016,7,14]],"date-time":"2016-07-14T00:00:00Z","timestamp":1468454400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2017,8]]},"abstract":"<jats:p>In this paper, we derive uniform convergence rates of nonparametric estimators for continuous time diffusion processes. In particular, we consider kernel-based estimators of the Nadaraya\u2013Watson type, introducing a new technical device called a<jats:italic>damping function<\/jats:italic>. This device allows us to derive sharp uniform rates over an infinite interval with minimal requirements on the processes: The existence of the moment of any order is not required and the boundedness of relevant functions can be significantly relaxed. Restrictions on kernel functions are also minimal: We allow for kernels with discontinuity, unbounded support, and slowly decaying tails. Our proofs proceed by using the covering-number technique from empirical process theory and exploiting the mixing and martingale properties of the processes. We also present new results on the path-continuity property of Brownian motions and diffusion processes over an infinite time horizon. These path-continuity results, which should also be of some independent interest, are used to control discretization biases of the nonparametric estimators. The obtained convergence results are useful for non\/semiparametric estimation and testing problems of diffusion processes.<\/jats:p>","DOI":"10.1017\/s0266466616000219","type":"journal-article","created":{"date-parts":[[2016,7,14]],"date-time":"2016-07-14T11:59:12Z","timestamp":1468497552000},"page":"874-914","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":6,"title":["UNIFORM CONVERGENCE RATES OF KERNEL-BASED NONPARAMETRIC ESTIMATORS FOR CONTINUOUS TIME DIFFUSION PROCESSES: A DAMPING FUNCTION APPROACH"],"prefix":"10.1017","volume":"33","author":[{"given":"Shin","family":"Kanaya","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,7,14]]},"reference":[{"key":"S0266466616000219_ref35","volume-title":"A Second Course in Stochastic 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