appendix

The auxiliary random vector of the parameter part is mainly constructed through inverse probability weighting and local correction methods, and its asymptotic normality is proved for the mixed sequence by combining the random error term Based on the constructed parameter part auxiliary random vector, the empirical logarithmic likelihood ratio function of the parameter part is obtained. At the same time, it is recommended to use penalty empirical likelihood (PEL) for variable selection. Under appropriate conditions, it is proved that the proposed penalty empirical estimation has Oracle characteristics and follows an asymptotic standard chi square distribution