20,171 research outputs found
Optimal sequential kernel detection for dependent processes
In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential nonparametric kernel procedures under local nonparametric alternatives. We prove a new theorem on the convergence of the normed delay of the associated sequential detection procedure which holds for dependent time series under a weak mixing condition. The result suggests a simple procedure to select a kernel from a finite set of candidate kernels, and therefore may also be of interest from a practical point of view. Further, we provide two new theorems about the existence and an explicit representation of optimal kernels minimizing the asymptotic normed delay. The results are illustrated by some examples. --Enzyme kinetics,financial econometrics,nonparametric regression,statistical genetics,quality control
Random walks - a sequential approach
In this paper sequential monitoring schemes to detect nonparametric drifts
are studied for the random walk case. The procedure is based on a kernel
smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson
estimator and its as- sociated sequential partial sum process under
non-standard sampling. The asymptotic behavior differs substantially from the
stationary situation, if there is a unit root (random walk component). To
obtain meaningful asymptotic results we consider local nonpara- metric
alternatives for the drift component. It turns out that the rate of convergence
at which the drift vanishes determines whether the asymptotic properties of the
monitoring procedure are determined by a deterministic or random function.
Further, we provide a theoretical result about the optimal kernel for a given
alternative
Sequential Data-Adaptive Bandwidth Selection by Cross-Validation for Nonparametric Prediction
We consider the problem of bandwidth selection by cross-validation from a
sequential point of view in a nonparametric regression model. Having in mind
that in applications one often aims at estimation, prediction and change
detection simultaneously, we investigate that approach for sequential kernel
smoothers in order to base these tasks on a single statistic. We provide
uniform weak laws of large numbers and weak consistency results for the
cross-validated bandwidth. Extensions to weakly dependent error terms are
discussed as well. The errors may be {\alpha}-mixing or L2-near epoch
dependent, which guarantees that the uniform convergence of the cross
validation sum and the consistency of the cross-validated bandwidth hold true
for a large class of time series. The method is illustrated by analyzing
photovoltaic data.Comment: 26 page
A METHODOLOGY FOR DETECTING BREAKS IN THE MEAN AND COVARIANCE STRUCTURE OF TIME SERIES
Some structural break techniques defined in the time and frequency domains are presented to explore, at the same time, the empirical evidence of the mean and covariance instability by uncovering regime-shifts in some inflation series. To that effect, we pursue a methodology that combines two approaches; the first is defined in the time domain and is designed to detect mean-shifts, and the second is defined in the frequency domain and is adopted to study the instability problem of the covariance function of the series. The proposed methodology has a double interest since, besides the detection of regime-shifts occasioned in the covariance structure of the series, it allows taking into account the presence of mean-shifts in this series. Note that unlike the works existing in the literature which often adopt a single technique to study the break identification problem, our methodology combines two approaches, parametric and nonparametric, to examine this problem.Structural change, mean and variance shifts, parametric and nonparametric approaches.
On detecting jumps in time series: Nonparametric setting
Motivated by applications in statistical quality control and signal analysis, we propose a sequential detection procedure which is designed to detect structural changes, in particular jumps, immediately. This is achieved by modifying a median filter by appropriate kernel-based jump preserving weights (shrinking) and a clipping mechanism. We aim at both robustness and immediate detection of jumps. Whereas the median approach ensures robust smooths when there are no jumps, the modification ensure immediate reaction to jumps. For general clipping location estimators we show that the procedure can detect jumps of certain heights with no delay, even when applied to Banach space valued data. For shrinking medians we provide an asymptotic upper bound for the normed delay. The finite sample properties are studied by simulations which show that our proposal outperforms classical procedures in certain respects. --Edge Detection,Nonparametric Estimation,Quality Control,Statistical Process Control
Online Nonparametric Anomaly Detection based on Geometric Entropy Minimization
We consider the online and nonparametric detection of abrupt and persistent
anomalies, such as a change in the regular system dynamics at a time instance
due to an anomalous event (e.g., a failure, a malicious activity). Combining
the simplicity of the nonparametric Geometric Entropy Minimization (GEM) method
with the timely detection capability of the Cumulative Sum (CUSUM) algorithm we
propose a computationally efficient online anomaly detection method that is
applicable to high-dimensional datasets, and at the same time achieve a
near-optimum average detection delay performance for a given false alarm
constraint. We provide new insights to both GEM and CUSUM, including new
asymptotic analysis for GEM, which enables soft decisions for outlier
detection, and a novel interpretation of CUSUM in terms of the discrepancy
theory, which helps us generalize it to the nonparametric GEM statistic. We
numerically show, using both simulated and real datasets, that the proposed
nonparametric algorithm attains a close performance to the clairvoyant
parametric CUSUM test.Comment: to appear in IEEE International Symposium on Information Theory
(ISIT) 201
Distributed Nonparametric Sequential Spectrum Sensing under Electromagnetic Interference
A nonparametric distributed sequential algorithm for quick detection of
spectral holes in a Cognitive Radio set up is proposed. Two or more local nodes
make decisions and inform the fusion centre (FC) over a reporting Multiple
Access Channel (MAC), which then makes the final decision. The local nodes use
energy detection and the FC uses mean detection in the presence of fading,
heavy-tailed electromagnetic interference (EMI) and outliers. The statistics of
the primary signal, channel gain or the EMI is not known. Different
nonparametric sequential algorithms are compared to choose appropriate
algorithms to be used at the local nodes and the FC. Modification of a recently
developed random walk test is selected for the local nodes for energy detection
as well as at the fusion centre for mean detection. It is shown via simulations
and analysis that the nonparametric distributed algorithm developed performs
well in the presence of fading, EMI and is robust to outliers. The algorithm is
iterative in nature making the computation and storage requirements minimal.Comment: 8 pages; 6 figures; Version 2 has the proofs for the theorems.
Version 3 contains a new section on approximation analysi
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