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ON JARQUE-BERA TESTS FOR ASSESSING MULTIVARIATE NORMALITY

Kazuyuki Koizumi, Okamoto Naoya, Takashi Seo

Open publisher page 33 citations

Abstract

In this paper, we consider some tests for the multivariate normality based on the sample measures of multivariate skewness and kurtosis. Sample measures of multivariate skewness and kurtosis were defined by Mardia [3], Srivastava [9] and so on. We derive new multivariate normality tests by using Mardia’s and Srivastava’s moments. For univariate case, Jarque and Bera [1] proposed bivariate test using skewness and kurtosis. We propose some new bivariate tests for assessing multivariate normality which are natural extensions of Jarque-Bera test. Finally, the numerical results by Monte Carlo simulation are shown in order to evaluate accuracy of expectations, variances and upper percentage points for new test statistics proposed in this paper.

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What this paper is about

In this paper, we consider some tests for the multivariate normality based on the sample measures of multivariate skewness and kurtosis. Sample measures of multivariate skewness and kurtosis were defined by Mardia [3], Srivastava [9] and so on. We derive new multivariate normality tests by using Mardia’s and Srivastava’s moments. For univariate case, Jarque and Bera [1] proposed bivariate test using skewness and kurtosis. We propose some new bivariate tests for assessing multivariate normality which are natural extensions of Jarque-Bera test. Finally, the numerical results by Monte Carlo simulation are shown in order to evaluate accuracy of expectations, variances and upper percentage points for new test statistics proposed in this paper.

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OpenAlex reports 33 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we consider some tests for the multivariate normality based on the sample measures of multivariate skewness and kurtosis. Sample measures of multivariate skewness and kurtosis were defined by Mardia [3], Srivastava [9] and so on. We derive new multivariate normality tests by using Mardia’s and Srivastava’s moments. For univariate case, Jarque and Bera [1] proposed bivariate test using skewness and kurtosis. We propose some new bivariate tests for assessing multivariate normality which are natural extensions of Jarque-Bera test. Finally, the numerical results by Monte Carlo simulation are shown in order to evaluate accuracy of expectations, variances and upper percentage points for new test statistics proposed in this paper.

Key concepts: Kurtosis, Multivariate statistics, Univariate, Bivariate analysis, Normality test, Statistics, Normality, Multivariate normal distribution

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