Abstract
We consider a partially observed two-dimensional diffusion process with coefficients depending on an unknown parameter and show the asymptotic nor-mality of the MLE and BE of this parameter in regular case. Then we estimate the parameters of nonregular models of increasing singularity The ßrst is the point of cusp of the trend coefficient of the ergodic diffusion process. Next is the problem of delay parameter estimation of a Gaussian ergodic processes, and the last is the problem of parameter estimation of a diffusion process with a discontinuous trend coefficient. In all these nonregular problems the rates of convergence are better than in the regular case, the asymptotic distributions of the estimators are not Gaussian and properties of the estimators are quite similar. The last section is devoted to models for which the conditions of ergodicity are not fulfilled.
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© 2004 Springer-Verlag London
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Kutoyants, Y.A. (2004). Special Models. In: Statistical Inference for Ergodic Diffusion Processes. Springer Series in Statistics. Springer, London. https://doi.org/10.1007/978-1-4471-3866-2_4
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DOI: https://doi.org/10.1007/978-1-4471-3866-2_4
Publisher Name: Springer, London
Print ISBN: 978-1-84996-906-2
Online ISBN: 978-1-4471-3866-2
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