Non-Concave Penalized Estimation Based on the Neighborhood Selection Method for Ising Model

In this paper, we put non-concave penalty on the local conditional likelihood. We obtain the oracle property and asymptotic normal distribution property of the parameters in Ising model. With a union band, we obtain the sign consistence for the estimator of parameter matrix, and the convergence speed under the matrix L_1 norm. The results of the simulation studies and a real data analysis show that the non-concave penalized estimator has larger sensitivity.