Spatial sign and rank covariance matricespackage:SpatialNPR Documentation

_S_p_a_t_i_a_l _s_i_g_n _a_n_d _r_a_n_k _c_o_v_a_r_i_a_n_c_e _m_a_t_r_i_c_e_s

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

     Functions to compute spatial sign, spatial symmetrized sign,
     spatial rank and  spatial signed rank covariance matrices

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

     SCov(X, location, na.action = na.fail)
     SSCov(X, na.action = na.fail)
     RCov(X, na.action = na.fail)
     SRCov(X, location, na.action = na.fail)

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

       X: matrix or a data frame

location: numeric vector (may be missing)

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:

     These functions compute the matrices of the form

                        ave {S(x_i) S^T(x_i)}

     where S(x_i) are the appropriate scores of the data: spatial
     signs, spatial symmetrized signs, spatial ranks or spatial signed
     ranks. These are the so called outer standardization matrices of
     location etc. tests based on spatial signs and ranks. They are not
     affine equivariant.

     'SCov' and 'SRCov' require a location vector with respect to which
     they are computed. If none is provided, vector of column means is
     used.

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

     Seija Sirkia, ssirkia@maths.jyu.fi

_S_e_e _A_l_s_o:

     spatial signs and ranks, corresponding shape matrices (inner
     standardization matrices)

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

     A<-matrix(c(1,2,-3,4,3,-2,-1,0,4),ncol=3)
     X<-matrix(rt(150,1),ncol=3)%*%t(A) 
     SCov(X) 
     SSCov(X) 
     RCov(X) 
     SRCov(X)
     to.shape(A%*%t(A),trace=1) 

