LAMN property for hidden processes: the case of integrated diffusions
In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the
statistical model given by the observation of local means of a diffusion process X. Our data
are given by∫ 1 0 X (s+i)/n dμ (s) for i= 0,..., n− 1 and the unknown parameter appears in the
diffusion coefficient of the process X only. Although the data are neither Markovian nor
Gaussian we can write down, with help of Malliavin calculus, an explicit expression for the
log-likelihood of the model, and then study the asymptotic expansion. We actually find that …
statistical model given by the observation of local means of a diffusion process X. Our data
are given by∫ 1 0 X (s+i)/n dμ (s) for i= 0,..., n− 1 and the unknown parameter appears in the
diffusion coefficient of the process X only. Although the data are neither Markovian nor
Gaussian we can write down, with help of Malliavin calculus, an explicit expression for the
log-likelihood of the model, and then study the asymptotic expansion. We actually find that …
Abstract
In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by∫ 1
0 X (s+i)/n dμ (s) for i= 0,..., n− 1 and the unknown parameter appears in the diffusion coefficient of the process X only. Although the data are neither Markovian nor Gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic expansion. We actually find that the asymptotic information of this model is the same one as for a usual discrete sampling of X.
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