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Zbl 0889.62072
Kent, John T.; Wood, Andrew T.A.
Estimating the fractal dimension of a locally self-similar Gaussian process by using increments.
(English)
[J] J. R. Stat. Soc., Ser. B 59, No.3, 679-699 (1997). ISSN 0035-9246

Summary: Consider the problem of estimating the parameter $\alpha$ of a stationary Gaussian process with covariance function $\sigma(t)= \sigma(0)- A|t|^\alpha +o(|t |^\alpha)$ as $|t|\to 0$, where $0<\alpha<2$. Conventional estimates based on an equally spaced sample of size $n$ on the interval $t\in[0,1]$ have the property that $\text {var} (\widehat \alpha)$ is of order $n^{-1}$ for $0<\alpha <3/2$, but of lower order $n^{2\alpha -4}$ for ${3\over 2} <\alpha <2$.\par The motivation for writing this paper is twofold: to produce estimators of $\alpha$ which have variance of order $n^{-1}$ for all $\alpha\in (0,2)$ and to gain a better understanding of a simulation anomaly, whereby estimators of $\alpha$ with variance of order $n^{2 \alpha-4}$ perform well in simulations when $\alpha$ is close to 2.
MSC 2000:
*62M09 Non-Markovian processes: estimation
62E20 Asymptotic distribution theory in statistics

Keywords: filtering; increments; intrinsic process; misspecification bias

Cited in: Zbl 0963.62090

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