cov4               package:ICS               R Documentation(latin1)

_S_c_a_t_t_e_r _M_a_t_r_i_x _b_a_s_e_d _o_n _F_o_u_r_t_h _M_o_m_e_n_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     Estimates the scatter matrix based on the 4th moments of the data.

_U_s_a_g_e:

     cov4(X, location = "Mean", na.action = na.fail)

_A_r_g_u_m_e_n_t_s:

       X: numeric data matrix or dataframe, missing values are not
          allowed. 

location: can be either 'Mean','Origin' or numeric. If numeric  the
          matrix is computed wrt to the given location.

na.action: a function which indicates what should happen when the data
          contain 'NA's.  Default is to fail.

_D_e_t_a_i_l_s:

     If location is 'Mean' the scatter matrix of 4th moments is
     computed wrt to the sample mean. For location = 'Origin' it is the
     scatter matrix of 4th moments wrt to the origin.  The scatter
     matrix is standardized in such a way to be consistent for the
     regular covariance matrix at the multinomal model. It is given for
     n x p matrix X by

            S= 1/(p+2) ave[r_i^2 (x_i-x_bar)'(x_i-x_bar)],

     where r_i is the Mahalanobis distance between x_i and the mean
     with respect to the regular covariance matrix.

_V_a_l_u_e:

     A matrix.

_A_u_t_h_o_r(_s):

     Klaus Nordhausen, klaus.nordhausen@uta.fi

_R_e_f_e_r_e_n_c_e_s:

     Cardoso, J.F. (1989), Source separation using higher order
     moments, in _Proc. IEEE Conf. on Acoustics, Speech and Signal
     Processing (ICASSP'89)_, 2109-2112.

     Oja, H., Sirkia, S. and Eriksson, J. (2006), Scatter matrices and
     independent component analysis, _Austrian Journal of Statistics_,
     *35*,  175-189.

_E_x_a_m_p_l_e_s:

     set.seed(654321)
     cov.matrix <- matrix(c(3,2,1,2,4,-0.5,1,-0.5,2), ncol=3)
     X <- rmvnorm(100, c(0,0,0), cov.matrix)
     cov4(X)
     cov4(X, location="Origin")
     rm(.Random.seed)

