bjtest                package:emplik                R Documentation

_T_e_s_t _t_h_e _B_u_c_k_l_e_y-_J_a_m_e_s _e_s_t_i_m_a_t_o_r _b_y _E_m_p_i_r_i_c_a_l _L_i_k_e_l_i_h_o_o_d

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

     Use the empirical likelihood ratio and Wilks theorem to test if
     the regression coefficient is equal to beta.

     The log empirical likelihood been maximized is

        sum_{d=1} log Delta F(e_i) + sum_{d=0} log [1-F(e_i)];

     where e_i are the residuals.

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

     bjtest(y, d, x, beta)

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

       y: a vector of length N, containing the censored responses.

       d: a vector (length N) of either 1's or 0's.  d=1 means y is
          uncensored; d=0 means y is right censored. 

       x: a matrix of size N by q. 

    beta: a vector of length q. The value of the regression 
          coefficient to be tested in the model  y_i = beta x_i  +
          epsilon_i 

_D_e_t_a_i_l_s:

     The above likelihood should be understood as the likelihood of the
      error term, so in the regression model the error epsilon should
     be iid.

     This version can handle the model where beta is a vector (of
     length q).

     The estimation equations used when maximize the  empirical
     likelihood is 

           0 = sum d_i Delta F(e_i) (x cdot m[,i])/(n w_i)

     which was described in detail in the reference below.

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

     A list with the following components: 

 "-2LLR": the -2 loglikelihood ratio; have approximate chisq 
          distribution under H_o.

  logel2: the log empirical likelihood, under estimating equation.

   logel: the log empirical likelihood of the Kaplan-Meier of e's.

    prob: the probabilities that max the empirical likelihood  under
          estimating equation.

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

     Mai Zhou.

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

     Buckley, J. and James, I. (1979). Linear regression with censored
     data. Biometrika,  *66* 429-36.

     Zhou, M. and Li, G. (2004). Empirical likelihood analysis of the
     Buckley-James estimator. Tech. Report.

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

     xx <- c(28,-44,29,30,26,27,22,23,33,16,24,29,24,40,21,31,34,-2,25,19)

