2,561 research outputs found
On line power spectra identification and whitening for the noise in interferometric gravitational wave detectors
In this paper we address both to the problem of identifying the noise Power
Spectral Density of interferometric detectors by parametric techniques and to
the problem of the whitening procedure of the sequence of data. We will
concentrate the study on a Power Spectral Density like the one of the
Italian-French detector VIRGO and we show that with a reasonable finite number
of parameters we succeed in modeling a spectrum like the theoretical one of
VIRGO, reproducing all its features. We propose also the use of adaptive
techniques to identify and to whiten on line the data of interferometric
detectors. We analyze the behavior of the adaptive techniques in the field of
stochastic gradient and in the
Least Squares ones.Comment: 28 pages, 21 figures, uses iopart.cls accepted for pubblication on
Classical and Quantum Gravit
Semiparametric stationarity and fractional unit roots tests based on data-driven multidimensional increment ratio statistics
In this paper, we show that the central limit theorem (CLT) satisfied by the
data-driven Multidimensional Increment Ratio (MIR) estimator of the memory
parameter d established in Bardet and Dola (2012) for d (--0.5, 0.5) can
be extended to a semiparametric class of Gaussian fractionally integrated
processes with memory parameter d (--0.5, 1.25). Since the asymptotic
variance of this CLT can be estimated, by data-driven MIR tests for the two
cases of stationarity and non-stationarity, so two tests are constructed
distinguishing the hypothesis d \textless{} 0.5 and d 0.5, as well as a
fractional unit roots test distinguishing the case d = 1 from the case d
\textless{} 1. Simulations done on numerous kinds of short-memory, long-memory
and non-stationary processes, show both the high accuracy and robustness of
this MIR estimator compared to those of usual semiparametric estimators. They
also attest of the reasonable efficiency of MIR tests compared to other usual
stationarity tests or fractional unit roots tests. Keywords: Gaussian
fractionally integrated processes; semiparametric estimators of the memory
parameter; test of long-memory; stationarity test; fractional unit roots test.Comment: arXiv admin note: substantial text overlap with arXiv:1207.245
A kepstrum approach to filtering, smoothing and prediction
The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization
where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new
approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to
adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the
type or order of the signal generating model. And unlike other approaches - with the exception of spectral
subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to
stationary signal and additive white noise
Recursive estimation of possibly misspecified MA(1) models: Convergence of a general algorithm
We introduce a recursive algorithm of conveniently general form for
estimating the coefficient of a moving average model of order one and obtain
convergence results for both correct and misspecified MA(1) models. The
algorithm encompasses Pseudolinear Regression (PLR--also referred to as AML and
) and Recursive Maximum Likelihood () without monitoring.
Stimulated by the approach of Hannan (1980), our convergence results are
obtained indirectly by showing that the recursive sequence can be approximated
by a sequence satisfying a recursion of simpler (Robbins-Monro) form for which
convergence results applicable to our situation have recently been obtained.Comment: Published at http://dx.doi.org/10.1214/074921706000000932 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
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