BLA                  package:mixAK                  R Documentation

_B_e_s_t _l_i_n_e_a_r _a_p_p_r_o_x_i_m_a_t_i_o_n _w_i_t_h _r_e_s_p_e_c_t _t_o _t_h_e _m_e_a_n _s_q_u_a_r_e _e_r_r_o_r
(_t_h_e_o_r_e_t_i_c_a_l _l_i_n_e_a_r _r_e_g_r_e_s_s_i_o_n).

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

     For a random vector X = (X[1], ..., X[p])' for which a mean and a
     covariance matrix are given computes coefficients of the best
     linear approximations with respect to the mean square error of
     each component of X given the remaining components of X.

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

     BLA(mean=c(0, 0),  Sigma=diag(2))

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

    mean: a numeric vector of means.

   Sigma: a covariance matrix.

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

     A list with the following components: 

    beta: computed regression coefficients

 sigmaR2: residual variances

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

     Arno&#353t Kom&#225rek arnost.komarek[AT]mff.cuni.cz

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

     And&#283l, J. (2007, odd. 2.5). Z&#225klady matematick&#233
     statistiky. Praha: MATFYZPRESS.

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

     ##### X = (U(1), U(2), U(3))'
     ##### * U(1) <= U(2) <= U(3)
     ##### * ordered uniform Unif(0, 1) variates
     EX <- (1:3)/4
     varX <- matrix(c(3,2,1, 2,4,2, 1,2,3), ncol=3)/80
     BLA(EX, Sigma=varX)

     ##### Uroda sena
     ##### * Y1 = uroda sena [cent/akr]
     ##### * Y2 = jarni srazky [palce]
     ##### * Y3 = kumulovana teplota nad 42 F
     EY <- c(28.02, 4.91, 28.7)
     varY <- matrix(c(19.54, 3.89, -3.76,  3.89, 1.21, -1.31,  -3.76, -1.31, 4.52), ncol=3)
     BLA(EY, Sigma=varY)

     ##### Z=(X, Y) ~ uniform distribution on a triangle
     ##### M = {(x,y): x>=0, y>=0, x+y<=3}
     EZ <- c(1, 1)
     varZ <- matrix(c(2, -1,  -1, 2), nrow=2)/4
     BLA(EZ, Sigma=varZ)

     ##### W=(X, Y) ~ uniform distribution on
     ##### M = {(x,y): x>=0, 0<=y<=1, y<=x<=y+1}
     EW <- c(1, 1/2)
     varW <- matrix(c(2, 1,  1, 1), nrow=2)/12
     BLA(EW, Sigma=varW)

