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Alexandre Brouste Marina Kleptsyna Alexandre Popier 《Statistical Inference for Stochastic Processes》2012,15(2):133-149
We consider a controlled linear differential equation which is partially observed with an additive fractional noise. In this setting, we study the asymptotic (for large observation time) design problem of the input and give an efficient estimator of the unknown signal drift parameter. The optimal estimation input is deduced. The consistency, asymptotic normality and convergence of the moments of the MLE are established. 相似文献
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In this paper we study the Maximum Likelihood Estimator (MLE) of the vector parameter of an autoregressive process of order p with regular stationary Gaussian noise. We prove the large sample asymptotic properties of the MLE under very mild conditions. We do simulations for fractional Gaussian noise (fGn), autoregressive noise (AR(1)) and moving average noise (MA(1)). 相似文献
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The paper studies long time asymptotic properties of the Maximum Likelihood Estimator (MLE) for the signal drift parameter
in a partially observed fractional diffusion system. Using the method of weak convergence of likelihoods due to Ibragimov
and Khasminskii (Statistics of random processes, 1981), consistency, asymptotic normality and convergence of the moments are
established for MLE. The proof is based on Laplace transform computations. 相似文献
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Efficient estimation of a non-Gaussian stable Lévy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a non-singular Fisher information matrix through the use of a non-diagonal norming matrix. The asymptotic normality and efficiency of a sequence of roots of the associated likelihood equation are shown as well. Moreover, we show that a simple preliminary method of moments can be used as an initial estimator of a scoring procedure, thereby conveniently enabling us to bypass numerically demanding likelihood optimization. Our simulation results show that the one-step estimator can exhibit quite similar finite-sample performance as the maximum likelihood estimator. 相似文献
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Brouste Alexandre Cai Chunhao Soltane Marius Wang Longmin 《Statistical Inference for Stochastic Processes》2020,23(2):301-318
The likelihood ratio test for a change in the mean-reverting parameter of a first order autoregressive model with stationary Gaussian noise is considered. The test statistic converges in distribution to the Gumbel extreme value distribution under the null hypothesis of no change-point for a large class of covariance structures including long-memory processes as the fractional Gaussian noise.
相似文献6.
This paper proposes consistent and asymptotically Gaussian estimators for the parameters $\lambda , \sigma $ and $H$ of the discretely observed fractional Ornstein–Uhlenbeck process solution of the stochastic differential equation $d Y_t = -\lambda Y_t dt + \sigma d W_t^H$ , where $(W_t^H, t\ge 0)$ is the fractional Brownian motion. For the estimation of the drift $\lambda $ , the results are obtained only in the case when $\frac{1}{2} < H < \frac{3}{4}$ . This paper also provides ready-to-use software for the R statistical environment based on the YUIMA package. 相似文献
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