On Construction of Higher Order Kernels Using Fourier Transforms and Covariance Functions

Abstract
In this paper, we show that a suitably chosen covariance function of a continuous time, second order stationary stochastic process can be viewed as a symmetric higher order kernel. This leads to the construction of a higher order kernel by choosing an appropriate covariance function. An optimal choice of the constructed higher order kernel that partially minimizes the mean integrated square error of the kernel density estimator is also discussed.

Acknowledgements
Research has been partially supported by ECR/2017/000374, Science & Engineering Research Board (SERB), Department of Science and Technology, Government of India. Research supported by INSPIRE fellowship, Department of Science and Technology, Government of India and a seed grant from IIT Bombay.

Publisher
arXiv

arXiv
2001.07383

Additional Links
https://arxiv.org/pdf/2001.07383

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