Penalized empirical likelihood for semiparametric models with a diverging number of parameters

- The methods EL and PEL for growing dimensional semiparametric models are proposed.
- The estimator based on EL has the asymptotic consistent property.
- PEL can be used to perform variable selection for growing dimensional sparse semiparametric models.

We apply empirical likelihood (EL) for high-dimensional semiparametric models and propose penalized empirical likelihood (PEL) method for parameter estimation and variable selection. It is shown that the estimator based on EL has the asymptotic consistent property, and that the limit distribution of the EL ratio statistic for the parameters θ is asymptotic normal distribution. Furthermore, in a high-dimensional setting, we prove that PEL in semiparametric models has the oracle property, that is, with probability tending to 1, the estimator based on PEL for the nonzero coefficients is efficient. Moreover, the PEL ratio statistic for the parameters θ is a χq2 distribution under the true null hypothesis. The performance of the proposed method is illustrated via a real data application and numerical simulations.