“…Second, functions to be estimated are directly estimated by the method of the kernel regression which locally approximates a target function by constant or linear functions (c.f., Fan and Gijbels, 1996). The local constant kernel regression, the so-called Nadaraya-Watson kernel estimation method, was originally applied to estimation of diffusion coefficients by Florens-Zmirou (1993), and since then its related theoretical and empirical studies have been carried out by many authors (i.e., Arapis and Gao, 2006;Bandi and Phillps, 2003;Jiang and Knight, 1997;Nicolau, 2003;Stanton, 1997). dX t = X t dt + X t dW t (1.1)…”