infill asymptotics
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2020 ◽  
pp. 1-44
Author(s):  
Jia Li ◽  
Yunxiao Liu

Abstract We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.


2019 ◽  
Vol 22 (3) ◽  
pp. 995-1008
Author(s):  
M. N. M. van Lieshout

AbstractWe investigate the asymptotic mean squared error of kernel estimators of the intensity function of a spatial point process. We derive expansions for the bias and variance in the scenario that n independent copies of a point process in $\mathbb {R}^{d}$ ℝ d are superposed. When the same bandwidth is used in all d dimensions, we show that an optimal bandwidth exists and is of the order n− 1/(d+ 4) under appropriate smoothness conditions on the true intensity function.


2008 ◽  
Vol 78 (18) ◽  
pp. 3145-3151 ◽  
Author(s):  
Zudi Lu ◽  
Dag Tjøstheim ◽  
Qiwei Yao

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