• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.463-475
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• 2021

Desgagné and de Micheaux (2018) proposed an alternative univariate normality test to the Jarque-Bera test. The proposed statistic is based on the sample second power skewness and kurtosis while the Jarque-Bera statistic uses sample Pearson's skewness and kurtosis that are the third and fourth standardized sample moments, respectively. In this paper, we generalize their statistic to a multivariate version based on orthogonalization or an empirical standardization of data. The proposed multivariate statistic follows chi-squared distribution approximately. A simulation study shows that the proposed statistic has good control of type I error even for a very small sample size when critical values from the approximate distribution are used. It has comparable power to the multivariate version of the Jarque-Bera test with exactly the same idea of the orthogonalization. It also shows much better power for some mixed normal alternatives.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.423-435
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• 2023

The Jarque and Bera (1980) statistic is one of the well known statistics to test univariate normality. It is based on the sample skewness and kurtosis which are the sample standardized third and fourth moments. Desgagné and de Micheaux (2018) proposed an alternative form of the Jarque-Bera statistic based on the sample second power skewness and kurtosis. In this paper, we generalize the statistic to a multivariate version by considering some data driven directions. They are directions given by the normalized standardized scaled residuals. The statistic is a modified multivariate version of Kim (2021), where the statistic is generalized using an empirical standardization of the scaled residuals of data. A simulation study reveals that the proposed statistic shows better power when the dimension of data is big.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.5
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• pp.305-310
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• 2003

In this paper, we proposed an IJADE(Improved joint approximate diagonalisation of eigenmatrices) which use high order statistics instead of second order statistics for data whitening. For simulation, we artificially construct signals mixed with two ECG signals, 60Hz power line interference and 16Hz sine signal and then put them into a JADE and an IJADE. To evaluate the performance of separated ECG signal in each algorithm, we have adopted indices such as kurtosis, standard deviation ratio, correlation coefficient and euclidean distance. As a results, IJ ADE showed theimproved performances as kurtosis of $2\%,$ standard deviation ratio of 0.2194, and Euclidean distance of 0.07 except correlation coefficient showing similar value. In conclusion, the proposed IJADE showed a good performance in separating ECG and a possibilities in applying to the various biological signal.

• Journal of Electrical Engineering and Technology
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• v.12 no.5
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• pp.1955-1962
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• 2017

Induction motors are a workhorse for the industry. The condition monitoring and fault analysis are the main concern for the engineers. The bearing is one of the vital segment of the induction machine and the condition of the whole machine is decided based on the condition of the bearing. In the present paper, the vibration signal of the bearing has been used for the analysis. The first line of action is to perform a statistical analysis of the vibration signal which gives trends in signal. To get the location of a fault in the bearing the second action is to develop an index based on Wavelet Packet Transform node energy named as Bearing Damage Index (BDI). Further, Teager-Kaiser Energy Operator (TKEO) has been calculated from higher index value to get the envelope and finally Power Spectral Density (PSD) has been applied to identify the fault frequencies. A performance index has also been developed to compare the usefulness of the proposed method with other existing methods. The result shows that the strong amplitude of fault characteristics and its side bands help to decide the type of fault present in the recorded signal obtained from the bearing.