A Least-Squares Approach to Consistent Information Estimation in Semiparametric Models

A method is proposed for consistent information estimation in a class of semiparametric models. The method is based on the geometric interpretation of the efficient score function, that it is the residual of the orthogonal projection of the score function for the finite-dimensional parameter onto the tangent space for the infinitedimensional parameter. The empirical version of this projection is a least-squares nonparametric regression problem. Under appropriate conditions, the sum of squared residuals of this regression is shown to be a consistent estimator of the efficient Fisher information and is actually the observed information for a class of sieve maximum likelihood estimators. Simulations studies are conducted to evaluate finite sample performance of the estimator in two illustrating examples: Poisson proportional mean model for panel count data and Cox model for interval-censored data. Finally the method is applied to two real-life examples: bladder tumor study and breast cosmesis study.