Minimax estimation of the diffusion coefficient through irregular samplings

Marc Hoffmann ()

Statistics & Probability Letters, 1997, vol. 32, issue 1, 11-24

Abstract: We study the problem of estimating the time dependent diffusion coefficient of a diffusion process in a nonparametric setting, when the sample path is observed at discrete times. We look at global Lp-error loss over a wide range of function spaces (namely, Besov spaces). We exhibit the minimax rate of convergence over linear estimators and provide estimators based on fast wavelets methods which are optimal. Our method takes into account functional estimation on the interval (with edges effects) and allows to consider irregular sampling schemes.

Keywords: Minimax; estimation; Diffusion; processes; Irregular; sampling; schemes; Wavelet; orthonormal; bases; Wavelets; on; the; interval; Besov; spaces (search for similar items in EconPapers)
Date: 1997
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