Abstract
In this paper, combining the threshold technique, we reconstruct Nadaraya-Watson estimation using Gamma asymmetric kernels for the unknown jump intensity function of a diffusion process with finite activity jumps. Under mild conditions, we obtain the asymptotic normality for the proposed estimator. Moreover, we have verified the better finite-sampling properties such as bias correction and efficiency gains of the underlying estimator compared with other nonparametric estimators through a Monte Carlo experiment.
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LIN Yi-wei is supported by the National Natural Science Foundation of China (No.11701331), Shandong Provincial Natural Science Foundation (No. ZR2017QA007) and Young Scholars Program of Shandong University. SONG Yu-** is supported by Ministry of Education, Humanities and Social Sciences project (No. 18YJCZH153), National Statistical Science Research Project (No. 2018LZ05), Youth Academic Backbone Cultivation Project of Shanghai Normal University (No. 310-AC7031-19-003021), General Research Fund of Shanghai Normal University (SK201720) and Key Subject of Quantitative Economics (No. 310-AC7031-19-004221) and Academic Innovation Team (No. 310-AC7031-19-004228) of Shanghai Normal University.
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Lin, Yw., Li, Zw. & Song, Yp. Bias Free Threshold Estimation for Jump Intensity Function. Appl. Math. J. Chin. Univ. 34, 309–325 (2019). https://doi.org/10.1007/s11766-019-3630-4
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DOI: https://doi.org/10.1007/s11766-019-3630-4