bjtest1d               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, _1-_d_i_m _o_n_l_y

_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)] .

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

     bjtest1d(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 of either 1's or 0's. d=1 means y is uncensored. d=0
          means y is right censored. 

       x: a vector of length N, covariate.

    beta: a number. the regression coefficient to  be tested in the
          model y = x beta + epsilon 

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

     In the above likelihood,  e_i = y_i - x * beta  is the residuals.

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

     A list with the following components: 

 "-2LLR": the -2 loglikelihood ratio; have approximate chi square 
          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 constraint.

_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.

     Owen, A. (1990). Empirical likelihood ratio confidence regions. 
     Ann. Statist. *18* 90-120.

_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)

