WRegTest               package:emplik               R Documentation

_T_e_s_t _t_h_e _c_a_s_e _w_e_i_g_h_t_e_d _r_e_g_r_e_s_s_i_o_n _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 'beta0',  by the case
     weighted estimation method.

     The log empirical likelihood been maximized is

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

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

     WRegTest(x, y, delta, beta0, psifun=function(t){t})

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

       x: a matrix of size N by q. Random design matrix. 

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

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

   beta0: a vector of length q. The value of the regression 
          coefficient to be tested in the linear model 

  psifun: the estimating function. The definition of it determines the
          type of estimator under testing. 

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

     The above likelihood should be understood as the likelihood of the
      censored responses 'y' and 'delta'. 

     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 delta_i Delta F(Y_i) X_i ( Y_i - X_i beta0 )

     which was described in detail in the reference below.

     For median regression (Least Absolute Deviation) estimator, you
     should define the  'psifun' as +1, -1 or 0 when t is >0, <0  or 
     =0.

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

     A list with the following components: 

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

   P-val: the p-value using the chi-square approximation.

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

     Mai Zhou.

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

     Zhou, M.; Bathke, A. and Kim, M. (2006).  Empirical likelihood
     analysis of the case weighted estimator in  heteroscastic AFT
     model. 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)

