20,669 research outputs found
Nonparametric spectral analysis with applications to seizure characterization using EEG time series
Understanding the seizure initiation process and its propagation pattern(s)
is a critical task in epilepsy research. Characteristics of the pre-seizure
electroencephalograms (EEGs) such as oscillating powers and high-frequency
activities are believed to be indicative of the seizure onset and spread
patterns. In this article, we analyze epileptic EEG time series using
nonparametric spectral estimation methods to extract information on
seizure-specific power and characteristic frequency [or frequency band(s)].
Because the EEGs may become nonstationary before seizure events, we develop
methods for both stationary and local stationary processes. Based on penalized
Whittle likelihood, we propose a direct generalized maximum likelihood (GML)
and generalized approximate cross-validation (GACV) methods to estimate
smoothing parameters in both smoothing spline spectrum estimation of a
stationary process and smoothing spline ANOVA time-varying spectrum estimation
of a locally stationary process. We also propose permutation methods to test if
a locally stationary process is stationary. Extensive simulations indicate that
the proposed direct methods, especially the direct GML, are stable and perform
better than other existing methods. We apply the proposed methods to the
intracranial electroencephalograms (IEEGs) of an epileptic patient to gain
insights into the seizure generation process.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS185 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Quantum metrology with open dynamical systems
This paper studies quantum limits to dynamical sensors in the presence of
decoherence. A modified purification approach is used to obtain tighter quantum
detection and estimation error bounds for optical phase sensing and
optomechanical force sensing. When optical loss is present, these bounds are
found to obey shot-noise scalings for arbitrary quantum states of light under
certain realistic conditions, thus ruling out the possibility of asymptotic
Heisenberg error scalings with respect to the average photon flux under those
conditions. The proposed bounds are expected to be approachable using current
quantum optics technology.Comment: v1: submitted to ISIT 2013, v2: updated with new results on detection
bounds, v3: minor update, submitted, v4: accepted by New J. Phy
Nonparametric Beta Kernel Estimator for Long Memory Time Series
The paper introduces a new nonparametric estimator of the spectral density that is given in smoothing the periodogram by the probability density of Beta random variable (Beta kernel). The estimator is proved to be bounded for short memory data, and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations suggest that the estimator automaticaly adapts to the long- or the short-range dependency of the process. A cross-validation procedure is also studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the reasonable performance of the estimation, and show that the data-driven estimator is a valuable tool for the detection of long-memory as well as hidden periodicities in stock returns.spectral density, long rage dependence, nonparametric estimation
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