scholarly journals Wavelet analysis and covariance structure of some classes of non-stationary processes

2000 ◽  
Vol 6 (4) ◽  
pp. 403-425 ◽  
Author(s):  
Charles-Antoine Guérin
Keyword(s):  
Wavelet Analysis ◽  
Covariance Structure ◽  
Stationary Processes

scholarly journals Significance tests for the wavelet power and the wavelet power spectrum

2007 ◽  
Vol 25 (11) ◽  
pp. 2259-2269 ◽  
Author(s):  
Z. Ge
Keyword(s):  
Wavelet Analysis ◽  
Power Spectrum ◽  
Lake Michigan ◽  
Random Noise ◽  
Gaussian White Noise ◽  
Covariance Structure ◽  
Sampling Period ◽  
Wavelet Power Spectrum ◽  
Significance Tests ◽  
Significance Levels

Abstract. Significance tests usually address the issue how to distinguish statistically significant results from those due to pure randomness when only one sample of the population is studied. This issue is also important when the results obtained using the wavelet analysis are to be interpreted. Torrence and Compo (1998) is one of the earliest works that has systematically discussed this problem. Their results, however, were based on Monte Carlo simulations, and hence, failed to unveil many interesting and important properties of the wavelet analysis. In the present work, the sampling distributions of the wavelet power and power spectrum of a Gaussian White Noise (GWN) were derived in a rigorous statistical framework, through which the significance tests for these two fundamental quantities in the wavelet analysis were established. It was found that the results given by Torrence and Compo (1998) are numerically accurate when adjusted by a factor of the sampling period, while some of their statements require reassessment. More importantly, the sampling distribution of the wavelet power spectrum of a GWN was found to be highly dependent on the local covariance structure of the wavelets, a fact that makes the significance levels intimately related to the specific wavelet family. In addition to simulated signals, the significance tests developed in this work were demonstrated on an actual wave elevation time series observed from a buoy on Lake Michigan. In this simple application in geophysics, we showed how proper significance tests helped to sort out physically meaningful peaks from those created by random noise. The derivations in the present work can be readily extended to other wavelet-based quantities or analyses using other wavelet families.

OPTIMAL QUADRATIC UNBIASED ESTIMATION FOR MODELS WITH LINEAR TOEPLITZ COVARIANCE STRUCTURE

Statistics ◽  
2003 ◽  
Vol 37 (1) ◽  
pp. 1-15
Author(s):  
JEAN-MICHEL MARIN ◽  
THIERRY DHORNE
Keyword(s):  
Covariance Structure ◽  
Unbiased Estimation

CAPABILITY MEASURES FOR m -DEPENDENT STATIONARY PROCESSES

Statistics ◽  
2003 ◽  
Vol 37 (1) ◽  
pp. 1-24 ◽  
Author(s):  
SY-MIEN CHEN ◽  
YU-SHENG HSU ◽  
W. L. PEARN
Keyword(s):  
Stationary Processes

Power of Modified Brown-Forsythe and Mixed-Model Approaches in Split-Plot Designs

Methodology ◽  
2017 ◽  
Vol 13 (1) ◽  
pp. 9-22 ◽  
Author(s):  
Pablo Livacic-Rojas ◽  
Guillermo Vallejo ◽  
Paula Fernández ◽  
Ellián Tuero-Herrero
Keyword(s):  
Repeated Measures ◽  
Statistical Power ◽  
Mixed Model ◽  
Covariance Structure ◽  
Simulation Method ◽  
Future Research ◽  
Repeated Measures Design ◽  
Fixed And Random Effects ◽  
Split Plot ◽  
High Level

Abstract. Low precision of the inferences of data analyzed with univariate or multivariate models of the Analysis of Variance (ANOVA) in repeated-measures design is associated to the absence of normality distribution of data, nonspherical covariance structures and free variation of the variance and covariance, the lack of knowledge of the error structure underlying the data, and the wrong choice of covariance structure from different selectors. In this study, levels of statistical power presented the Modified Brown Forsythe (MBF) and two procedures with the Mixed-Model Approaches (the Akaike’s Criterion, the Correctly Identified Model [CIM]) are compared. The data were analyzed using Monte Carlo simulation method with the statistical package SAS 9.2, a split-plot design, and considering six manipulated variables. The results show that the procedures exhibit high statistical power levels for within and interactional effects, and moderate and low levels for the between-groups effects under the different conditions analyzed. For the latter, only the Modified Brown Forsythe shows high level of power mainly for groups with 30 cases and Unstructured (UN) and Autoregressive Heterogeneity (ARH) matrices. For this reason, we recommend using this procedure since it exhibits higher levels of power for all effects and does not require a matrix type that underlies the structure of the data. Future research needs to be done in order to compare the power with corrected selectors using single-level and multilevel designs for fixed and random effects.

Classification of Acceleration Waveforms during Walking by Wavelet Transform

1997 ◽  
Vol 36 (04/05) ◽  
pp. 356-359 ◽  
Author(s):  
M. Sekine ◽  
M. Ogawa ◽  
T. Togawa ◽  
Y. Fukui ◽  
T. Tamura
Keyword(s):  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Center Of Gravity ◽  
Dynamic Responses ◽  
Sequential Data ◽  
Acceleration Signal ◽  
Continuous Dynamic

Abstract:In this study we have attempted to classify the acceleration signal, while walking both at horizontal level, and upstairs and downstairs, using wavelet analysis. The acceleration signal close to the body’s center of gravity was measured while the subjects walked in a corridor and up and down a stairway. The data for four steps were analyzed and the Daubecies 3 wavelet transform was applied to the sequential data. The variables to be discriminated were the waveforms related to levels -4 and -5. The sum of the square values at each step was compared at levels -4 and -5. Downstairs walking could be discriminated from other types of walking, showing the largest value for level -5. Walking at horizontal level was compared with upstairs walking for level -4. It was possible to discriminate the continuous dynamic responses to walking by the wavelet transform.

Study of Identification Method of Drunk Driving Based on Wavelet Analysis

ICCTP 2011 ◽  
2011 ◽  
Author(s):  
Xing-jian Zhang ◽  
Xiao-hua Zhao ◽  
Jian Rong ◽  
Shi-li Xu
Keyword(s):  
Wavelet Analysis ◽  
Drunk Driving ◽  
Identification Method

Efficiency of application of the phase-chronometric method and neurodiagnostics for monitoring the degradation of rolling bearings during operation

2020 ◽  
pp. 43-50
Author(s):  
A.S. Komshin ◽  
K.G. Potapov ◽  
V.I. Pronyakin ◽  
A.B. Syritskii
Keyword(s):  
Life Cycle ◽  
Wavelet Analysis ◽  
Metrological Support ◽  
Rolling Bearing ◽  
Technical Condition ◽  
Measurement Information ◽  
Rolling Bearings ◽  
Vibration Diagnostics ◽  
Bearing Life ◽  
Alternative Approach

The paper presents an alternative approach to metrological support and assessment of the technical condition of rolling bearings in operation. The analysis of existing approaches, including methods of vibration diagnostics, envelope analysis, wavelet analysis, etc. Considers the possibility of applying a phase-chronometric method for support on the basis of neurodiagnostics bearing life cycle on the basis of the unified format of measurement information. The possibility of diagnosing a rolling bearing when analyzing measurement information from the shaft and separator was evaluated.

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