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Notes on Estimating Inverse-Gaussian and Gamma Subordinators under High-frequency Sampling

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概要 We study joint efficient estimation of two parameters dominating gamma and inverse-Gaussian subordinators, based on discrete observations sampled at $ (t^n_ i)^n_{i=1} $ satisfying $ h_n := max_{i leq... n}(t^n_i - t^n_{i-1}) \rigtarrow 0 $ as $ n \rightarrow infty $. Under the condition that $ T_n := t^n_n \rigtarrow infty $ as $ n \rightarrow infty $ we have two kinds of optimal rates, $ sqrt{n} $ and $ sqrt{T_n} $, and especially. Moreover, as in estimation of diffusion coefficient of a Wiener process the $ sqrt{n} $-consistent component of the estimator is effectively workable even when $ T_n $ does not tend to infinity. Simulation experiments are given under several $ h_n $’s behaviors続きを見る

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登録日 2009.04.22
更新日 2018.02.26