Exponentially tilted likelihood inference on growing dimensional unconditional moment models

Abstract

Growing-dimensional data with likelihood unavailable are often encountered in various fields. This paper presents a penalized exponentially tilted likelihood (PETL) for variable selection and parameter estimation for growing dimensional unconditional moment models in the presence of correlation among variables and model misspecifica- tion. Under some regularity conditions, we investigate the consistent and oracle proper- ties of the PETL estimators of parameters, and show that the constrainedly PETL ratio statistic for testing contrast hypothesis asymptotically follows the central chi-squared distribution. Theoretical results reveal that the PETL approach is robust to model mis- specification. We also study high-order asymptotic properties of the proposed PETL estimators. Simulation studies are conducted to investigate the finite performance of the proposed methodologies. An example from the Boston Housing Study is illustrated.

References in corpus (2)

• On the adaptive elastic-net with a diverging number of parameters
• Nonparametric methods for inference in the presence of instrumental variables