Non Parametric Estimation of Second-Order Diffusion Equation by Using Asymmetric Kernels

Muhammad Hanif

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 9, 1896-1910

Abstract: In this paper, we study the non parametric estimation of drift coefficient and diffusion coefficient in the second-order diffusion equation by using the asymmetric kernel functions, based on the difference of discrete time observations. The basic idea relies upon replacing the symmetric kernel by asymmetric kernel and provides a new way of obtaining the non parametric estimation for second-order diffusion equation. Under the appropriate assumptions, we prove that the proposed estimators of second-order diffusion equation are consistent and asymptotically follow normal distribution.

Date: 2015
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DOI: 10.1080/03610926.2012.756915

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