15,788 research outputs found
Estimation of fractal dimension for a class of Non-Gaussian stationary processes and fields
We present the asymptotic distribution theory for a class of increment-based
estimators of the fractal dimension of a random field of the form g{X(t)},
where g:R\to R is an unknown smooth function and X(t) is a real-valued
stationary Gaussian field on R^d, d=1 or 2, whose covariance function obeys a
power law at the origin. The relevant theoretical framework here is ``fixed
domain'' (or ``infill'') asymptotics. Surprisingly, the limit theory in this
non-Gaussian case is somewhat richer than in the Gaussian case (the latter is
recovered when g is affine), in part because estimators of the type considered
may have an asymptotic variance which is random in the limit. Broadly, when g
is smooth and nonaffine, three types of limit distributions can arise, types
(i), (ii) and (iii), say. Each type can be represented as a random integral.
More specifically, type (i) can be represented as the integral of a certain
random function with respect to Lebesgue measure; type (ii) can be represented
as the integral of a second random functio
Testing for Changes in Kendall's Tau
For a bivariate time series we want to detect
whether the correlation between and stays constant for all . We propose a nonparametric change-point test statistic based on
Kendall's tau and derive its asymptotic distribution under the null hypothesis
of no change by means a new U-statistic invariance principle for dependent
processes. The asymptotic distribution depends on the long run variance of
Kendall's tau, for which we propose an estimator and show its consistency.
Furthermore, assuming a single change-point, we show that the location of the
change-point is consistently estimated. Kendall's tau possesses a high
efficiency at the normal distribution, as compared to the normal maximum
likelihood estimator, Pearson's moment correlation coefficient. Contrary to
Pearson's correlation coefficient, it has excellent robustness properties and
shows no loss in efficiency at heavy-tailed distributions. We assume the data
to be stationary and P-near epoch dependent on an
absolutely regular process. The P-near epoch dependence condition constitutes a
generalization of the usually considered -near epoch dependence, , that does not require the existence of any moments. It is therefore very
well suited for our objective to efficiently detect changes in correlation for
arbitrarily heavy-tailed data
Adaptive wavelet based estimator of the memory parameter for stationary Gaussian processes
This work is intended as a contribution to a wavelet-based adaptive estimator
of the memory parameter in the classical semi-parametric framework for Gaussian
stationary processes. In particular we introduce and develop the choice of a
data-driven optimal bandwidth. Moreover, we establish a central limit theorem
for the estimator of the memory parameter with the minimax rate of convergence
(up to a logarithm factor). The quality of the estimators are attested by
simulations
An efficient semiparametric maxima estimator of the extremal index
The extremal index , a measure of the degree of local dependence in
the extremes of a stationary process, plays an important role in extreme value
analyses. We estimate semiparametrically, using the relationship
between the distribution of block maxima and the marginal distribution of a
process to define a semiparametric model. We show that these semiparametric
estimators are simpler and substantially more efficient than their parametric
counterparts. We seek to improve efficiency further using maxima over sliding
blocks. A simulation study shows that the semiparametric estimators are
competitive with the leading estimators. An application to sea-surge heights
combines inferences about with a standard extreme value analysis of
block maxima to estimate marginal quantiles.Comment: 17 pages, 7 figures. Minor edits made to version 1 prior to journal
publication. The final publication is available at Springer via
http://dx.doi.org/10.1007/s10687-015-0221-
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