rqmcmb                package:rqmcmb2                R Documentation

_M_a_r_k_o_v _C_h_a_i_n _M_a_r_g_i_n_a_l _B_o_o_t_s_t_r_a_p _f_o_r _Q_u_a_n_t_i_l_e
_R_e_g_r_e_s_s_i_o_n

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

     MCMB for Quantile Regression (also see quantreg package by Roger
     Koenker)

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

     rqmcmb(x=x, y=y, tau=0.5, K=100, int=TRUE,
     plotTheta=FALSE)

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

       x: a data matrix (n by p) for the design variables whose rows
          correspond to cases

       y: a response vector of length n

     tau: a percentile level between 0 and 1. Default at 0.5 for the
          median

       K: length of the MCMB sequence. Default is 100

plotTheta: TRUE or FALSE for plotting the MCMB sequence. Default to
          FALSE

     int: should be set to TRUE if the intercept is to be included in
          the model, and  to FALSE if no intercept is desired. Default
          is TRUE.

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

     A list with the following components: 

    coef: the parameter estimate from rq()

   theta: a matrix containing the MCMB sequence. The first row is  the
          initial  parameter estimate from rq()

 success: returns 1 if MCMB is successful.  A value of 0  indicates
          that the program fails to return a desired MCMB sequence

      cn: condition number of the X'X matrix.

_W_A_R_N_I_N_G:

     The MCMB may not be suitable for problems of small sample sizes.
     Severe collinearity in the x matrix could also be harmful.

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

     Maria Kocherginsky (mkocherg@health.bsd.uchicago.edu) and Xuming
     He (x-he@uiuc.edu)

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

     Kocherginsky, M. (2003). Extensions of Markov Chain Marginal
     Bootstrap. Ph.D Thesis, University of Illinois Urbana-Champaign.

     Kocherginsky, M., He, X. and Mu, Y. (2003). Practical Confidence
     Intervals for Regression Quantiles. Preprint.

     He, X. and Hu, F. (2002). Markov Chain Marginal Bootstrap. 
     Journal of the American Statistical Association , Vol. 97, no.
     459,  783-795.

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

     'rq'

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

       library(quantreg)
       
       x <- cbind(rnorm(100), runif(100))
       y <- rnorm(100)

       #generate the MCMB sequence:
       mcmb <- rqmcmb(x, y, tau=.5, plotTheta=FALSE)

       #get MCMB estimates of mean, SD, and CI:
       rqmcmb.ci(mcmb)

       #plot the MCMB sequences:
       rqmcmb.plot(mcmb)
       

