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.
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LI Fanqun; YANG Guiyuan; ZHANG Kongsheng. Non-Concave Penalized Estimation Based on the Neighborhood Selection Method for Ising Model. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2019, 35(2): 165-177.