Nonparametric Statistical Inference for i.i.d. Sparsely Observed Diffusions: an FDA Perspective
N. Mohammadi, V. Panaretos, L. Santoro
FDA covers a central role in studying different inference problems, allowing to consider functional datasets on complex domains. For discrete observations, this approach basically imposes some smoothness conditions on the sample paths and/or their covariance function to apply approximating methods. However, the usual regularity assumptions limit the appropriateness of FDA in many common settings, most notably SDE. We introduce a modification of existing methods, dubbed the reflected triangle estimator and make inferences about the global behavior of the diffusion processes. We show that this allows for the FDA of processes with nowhere differentiable sample paths, even when these are discretely and noisily observed. We then relate the global behavior of the processes to their local behavior by means of a novel PDE. We establish almost sure uniform asymptotic convergence rates of the proposed estimators as the number of observed curves grows to infinity.
Keywords: Brownian motion, FDA, Ito diffusion process, Local polynomial regression, reflected triangle, Sparse sampling, SDE Local linear smoothing
Scheduled
GT06 Functional Data Analysis IV. Functional Time Series
June 9, 2022 10:10 AM
Grade Hall
Other papers in the same session
J. Álvarez Liébana, W. González Manteiga, M. D. Ruiz Medina
A. Caponera, J. Fageot, M. Simeoni, V. M. Panaretos
F. D. Miranda Huaynalaya, M. D. Ruiz Medina
A. Torres Signes, M. P. Frías Bustamante, M. D. Ruiz Medina
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6/8/22
Visit Alhambra
Tomorrow, Thursday, we will visit the Alhambra. 1. At 7:00 p.m., buses will start leaving from the door of the Hotel Granada Center (in front of the door of the Faculty of Sciences) 2. Upon arrival, groups with guides will be organized. 3. There will be groups in English language. These groups will wait at the destination until the arrival of all buses. 4. After the visit to the Alhambra we will walk to the Carmen de los Mártires to have a cocktail. 5. On the way back, we can go back by bus, which will leave from the same place where they left us at the Alhambra. 6. Although the way to the Alhambra by bus seems long, it really is close to the city. We invite you, whoever wishes, to go down for a pleasant walk. 7. Do not forget to take your Alhambra ticket and your identity card or passport. The document must be the same whose number matches the ticket number you have.
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5/31/22
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5/27/22
Gala Dinner
It opens the possibility that anyone who is registered for the conference, and wants non-registered companions to attend the gala dinner, can do so by paying the price of this dinner (80 euros VAT included). This payment must be made before June 1 (inclusive). To do this, contact with [email protected]
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5/23/22
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To access the Alhambra on the visit on Thursday 9, it is obligatory to present the identification document whose reference was sent to the organization (eurocongress)
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5/16/22
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