maryo                 package:rrcov                 R Documentation

_M_a_r_o_n_a _a_n_d _Y_o_h_a_i _A_r_t_i_f_i_c_i_a_l _D_a_t_a

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

     Simple artificial data set generated according the example by 
     Marona and Yohai (1998).  The data set consists of 20 bivariate
     normal observations generated with zero means, unit variances and
     correlation 0.8. The sample  correlation is 0.81. Two outliers are
     introduced (i.e. these are  10% of the data) in the following way:
     two points are modified  by interchanging the largest (observation
     19) and smallest  (observation 9) value of the first coordinate.
     The sample correlation  becomes 0.05.  This example  provides a
     good example of the fact that a  multivariate outlier need not be
     an outlier in any of its  coordinate variables.

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

     data(maryo)

_F_o_r_m_a_t:

     A data frame with 20 observations on 2 variables. To introduce the
     outliers x[9,1] with x[19,1] are interchanged.

_S_o_u_r_c_e:

     R. A. Marona and V. J. Yohai (1998) Robust estimation of
     multivariate  location and scatter. In _Encyclopedia of
     Statistical Sciences, Updated Volume 2_  (Eds. S.Kotz, C.Read and
     D.Banks). Wiley, New York p. 590

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

     data(maryo)
     getCorr(Cov(maryo))       ## the sample correlation is 0.81

     ## Modify 10
     ##  modify two points (out of 20) by interchanging the 
     ##  largest and smallest value of the first coordinate
     imin <- which(maryo[,1]==min(maryo[,1]))        # imin = 9
     imax <- which(maryo[,1]==max(maryo[,1]))        # imax = 19
     maryo1 <- maryo
     maryo1[imin,1] <- maryo[imax,1]
     maryo1[imax,1] <- maryo[imin,1]

     ##  The sample correlation becomes 0.05
     plot(maryo1)
     getCorr(Cov(maryo1))             ## the sample correlation becomes 0.05
     cov2cor(covMcd(maryo1)$cov)      ## the (reweighted) MCD correlation is 0.79

