Shape matrices           package:SpatialNP           R Documentation

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

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

     Iterative algorithms to find shape matrices based on spatial signs
     and ranks and the k-step versions of these.

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

      

     rank.shape(X, init = NULL, steps = Inf, eps = 1e-06, maxiter = 100,
     na.action = na.fail)

     signrank.shape(X, location = NULL, init = NULL, steps = Inf, eps =
     1e-06, maxiter = 100, na.action = na.fail)

     spatial.shape(X, score = c("sign", "symmsign", "rank", "signrank"),
     location = NULL, init = NULL, steps = Inf, eps = 1e-06, maxiter = 100,
     na.action = na.fail)

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

       X: a matrix or a data frame 

   score: a character string indicating which transformation of the
          observations should be used

location: an optional vector giving the location of the data

    init: an optional starting value for the iteration

   steps: fixed number of iteration steps to take, if 'Inf' iteration
          is repeated until convergence (or until 'maxiter' steps)

     eps: tolerance for convergence

 maxiter: maximum number of iteration steps. Ignored if 'steps'  is
          finite

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:

     As 'tyler.shape' for spatial signs and 'duembgen.shape' for
     spatial symmetrized signs, but for spatial ranks and signed ranks.
     These are the so called inner standardization matrices of location
     etc. tests based on spatial signs and ranks. When data is
     standardized using these matrices the corresponding sign or rank
     scores will appear "uncorrelated": the corresponding outer
     standardization matrices will be proportional to the identity
     matrix, see examples.

     'spatial.shape' is a wrapper function for a unified access to all
     four shape estimates. The choice of estimate is done via 'score':

     *  '"sign"' for 'tyler.shape' 

     *  '"symmsign"' for 'duembgen.shape'  .ti *  '"rank"' for
        'rank.shape'  .ti *  '"signrank"' for 'signrank.shape'

        'signrank.shape' (and 'tyler.shape', thus also 'spatial.shape')
        requires the location vector with respect to which it is
        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:

     'tyler.shape', 'duembgen.shape', also spatial sign and rank
     covariance matrices and spatial signs and ranks

_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)
     signrank.shape(X)
     spatial.shape(X,score="sign")
     to.shape(A%*%t(A))
     # one-step shape estimate based on spatial ranks and covariance matrix:
     spatial.shape(X,score="rank",init=cov(X),steps=1)
     # effect of inner standardization:
     RCov(X)
     RCov(X%*%t(chol(solve(rank.shape(X)))))

