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Dependent Data (dependent + data)

Distribution by Scientific Domains
Mathematics and Statistics57%

Selected Abstracts

Resampling Methods for Dependent Data

BIOMETRICS, Issue 2 2006
Joerg Trommer
No abstract is available for this article. [source]

A Three-step Method for Choosing the Number of Bootstrap Repetitions

ECONOMETRICA, Issue 1 2000
Donald W. K. Andrews
This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, confidence regions, hypothesis tests, p -values, and bias correction. For each of these problems, the paper provides a three-step method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval length, test's critical value, test's p -value, or bias-corrected estimate based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B=,. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals. Monte Carlo simulations show that the proposed methods work very well. [source]

Estimating the number of independent components for functional magnetic resonance imaging data

HUMAN BRAIN MAPPING, Issue 11 2007
Yi-Ou Li
Abstract Multivariate analysis methods such as independent component analysis (ICA) have been applied to the analysis of functional magnetic resonance imaging (fMRI) data to study brain function. Because of the high dimensionality and high noise level of the fMRI data, order selection, i.e., estimation of the number of informative components, is critical to reduce over/underfitting in such methods. Dependence among fMRI data samples in the spatial and temporal domain limits the usefulness of the practical formulations of information-theoretic criteria (ITC) for order selection, since they are based on likelihood of independent and identically distributed (i.i.d.) data samples. To address this issue, we propose a subsampling scheme to obtain a set of effectively i.i.d. samples from the dependent data samples and apply the ITC formulas to the effectively i.i.d. sample set for order selection. We apply the proposed method on the simulated data and show that it significantly improves the accuracy of order selection from dependent data. We also perform order selection on fMRI data from a visuomotor task and show that the proposed method alleviates the over-estimation on the number of brain sources due to the intrinsic smoothness and the smooth preprocessing of fMRI data. We use the software package ICASSO (Himberg et al. [ 2004]: Neuroimage 22:1214,1222) to analyze the independent component (IC) estimates at different orders and show that, when ICA is performed at overestimated orders, the stability of the IC estimates decreases and the estimation of task related brain activations show degradation. Hum Brain Mapp, 2007. © 2007 Wiley-Liss, Inc. [source]

Thermal Shock Resistance of an AlN,BN,SiC Ceramic

JOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 6 2009
Andrew A. Buchheit
Mechanical and thermal properties of AlN,BN,SiC (ABS) ceramics were used to calculate the R, R,, and R,, thermal shock parameters. The R parameter values ranged from ,400° to 450°C. Specimens were thermal shocked by water quenching and the critical quench temperatures (,TC) were compared with those of a baseline SiC composition. The behavior of the ABS was predicted by R parameter calculations while the behavior of the baseline material was predicted by the R, calculations due to its higher thermal conductivity (87 W·(m·K) -1) as compared with the ABS materials (,30 W·(m·K),1). The highest critical quench temperature for ABS was ,415°C with the lowest at 360°C, while the critical quench temperature for the baseline material was 450°C. Using temperature dependent data over an appropriate temperature range (room temperature to the predicted ,TC), the R parameters of the ABS materials were within 15°C of predictions. The baseline material was ,1.7 times higher than predicted and this was attributed to the high-thermal conductivity of the material resulting in soft thermal shock during quench testing. [source]

Asymptotic self-similarity and wavelet estimation for long-range dependent fractional autoregressive integrated moving average time series with stable innovations

JOURNAL OF TIME SERIES ANALYSIS, Issue 2 2005
Stilian Stoev
Primary 60G18; 60E07; Secondary 62M10; 63G20 Abstract., Methods for parameter estimation in the presence of long-range dependence and heavy tails are scarce. Fractional autoregressive integrated moving average (FARIMA) time series for positive values of the fractional differencing exponent d can be used to model long-range dependence in the case of heavy-tailed distributions. In this paper, we focus on the estimation of the Hurst parameter H = d + 1/, for long-range dependent FARIMA time series with symmetric , -stable (1 < , < 2) innovations. We establish the consistency and the asymptotic normality of two types of wavelet estimators of the parameter H. We do so by exploiting the fact that the integrated series is asymptotically self-similar with parameter H. When the parameter , is known, we also obtain consistent and asymptotically normal estimators for the fractional differencing exponent d = H , 1/,. Our results hold for a larger class of causal linear processes with stable symmetric innovations. As the wavelet-based estimation method used here is semi-parametric, it allows for a more robust treatment of long-range dependent data than parametric methods. [source]

Prediction and nonparametric estimation for time series with heavy tails

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2002
PETER HALL
Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on `local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional `local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares methods based on linear fits, the order of magnitude of variance does not depend on tail-weight of the error distribution. To make these points clear, we develop theory describing local applications to time series of both least-squares and least-absolute-deviations methods, showing for example that, in the case of heavy-tailed data, the conventional local-linear least-squares estimator suffers from an additional bias term as well as increased variance. [source]

On the estimation of the heavy-tail exponent in time series using the max-spectrum

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2010
Stilian A. Stoev
Abstract This paper addresses the problem of estimating the tail index , of distributions with heavy, Pareto-type tails for dependent data, that is of interest in the areas of finance, insurance, environmental monitoring and teletraffic analysis. A novel approach based on the max self-similarity scaling behavior of block maxima is introduced. The method exploits the increasing lack of dependence of maxima over large size blocks, which proves useful for time series data. We establish the consistency and asymptotic normality of the proposed max-spectrum estimator for a large class of m -dependent time series, in the regime of intermediate block-maxima. In the regime of large block-maxima, we demonstrate the distributional consistency of the estimator for a broad range of time series models including linear processes. The max-spectrum estimator is a robust and computationally efficient tool, which provides a novel time-scale perspective to the estimation of the tail exponents. Its performance is illustrated over synthetic and real data sets. Copyright © 2009 John Wiley & Sons, Ltd. [source]