Kurt-package {Kurt}

Kurt: Performs kurtosis-based statistical analyses

Description

Computes measures of multivariate kurtosis, matrices of fourth-order moments and cumulants, kurtosis-based projection pursuit

Details

Index of help topics:

Cum4                    Cum4: fourth multivariate cumulant
ExtKur                  ExtKur: kurtosis based projection pursuit
ExtKurBiv               ExtKurBiv: kurtosis-based projection pursuit
                        for bivariate random vectors
Fourth                  Fourth: matrices of fourth moments or fourth
                        cumulants
Fourth4                 Fourth4: fourth moment of a data matrix
Kurt-package            Kurt: Performs kurtosis-based statistical
                        analyses
NoKurt                  NoKurt: data projections whose excess kurtosis
                        is as close to zero as possible
ScalarKurt              ScalarKurt
optik                   optik

ScalarKurt(), ExtKurt(), ExtKurtBiv(), optik(), NoKurt(), Cum4(), Fourth(), Fourth4()

Author(s)

Cinzia Franceschini and Nicola Loperfido

Maintainer: Cinzia Franceschini [e-mail]

References

Franceschini, C. and Loperfido, N. (2012). On some Inequalities between Measures of Multivariate Kurtosis, with Application to Financial Returns. In "Mathematical and Statistical Methods for Actuarial Sciences and Finance", Perna, C. and Sibillo, M. (Eds.), Springer, 211-218.

Franceschini, C. and Loperfido, N. (2018). An Algorithm for Finding Projections with Extreme Kurtosis. In "Studies in Theoretical and Applied Statistics: SIS2016-48th Meeting of the Italian Statistical Society, Salerno 8-10 June 2016", Perna C., Pratesi M. and Ruiz-Gazen A. (Eds.), Springer.

Henze, N. (1994). On Mardia's kurtosis test for multivariate normality. Communications in statistics-Theory and Methods 23:4, 1031-1045.

Kollo, T. (2008). Multivariate skewness and kurtosis measures with an application in ICA. Journal of Multivariate Analysis 99, 2328-2338.

Kollo, T. and Srivastava, M.S. (2005). Estimation and testing of parameters in multivariate Laplace distribution. Comm. Statist. 33, 2363–2687.

Koziol, J.A. (1987). An alternative formulation of Neyman's smooth goodness of fit tests under composite alternatives. Metrika 34, 17-24.

Koziol, J.A. (1989). A note on measures of multivariate kurtosis. Biometrical Journal 31, 619-624.

Loperfido, N. (2011). Spectral Analysis of the Fourth Moment Matrix. Linear Algebra and its Applications 435, 1837-1844.

Loperfido, N. (2014). A Note on the Fourth Cumulant of a Finite Mixture Distribution. Journal of Multivariate Analysis 123, 386-394.

Loperfido, N. (2017). A New Kurtosis Matrix, with Statistical Applications. Linear Algebra and its Applications 512, 1-17.

Loperfido N. (2019). Kurtosis-Based Projection Pursuit for Outlier Detection in Financial Time Series. The European Journal of Finance, to appear.

Loperfido, N. (2020). Some Remarks on Koziol's Kurtosis. Journal of Multivariate Analysis 175, to appear.

Malkovich, J.F. and Afifi, A.A. (1973). On Tests for Multivariate Normality. J. Amer. Statist. Ass. 68, 176-179.

Mardia, K.V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika 57, 519-530.

Mardia, K. V. and Kent, J. T. (1991). Rao Score Tests for Goodness of Fit and Independence. Biometrika 78, 355-36.

Miettinen J., Taskinen S., Nordhausen K. and Oja H. (2015). Fourth Moments and Independent Component Analysis. Statistical Science 30, 372-390.

Mori T.F., Rohatgi V.K. and Szekely G.J. (1993). On multivariate skewness and kurtosis. Theory Probab. Appl. 38, 547-551.