🤖 AI Summary
This study addresses the estimation and inference of functional coefficients in varying-coefficient models under Laguerre–Sobolev spaces. By approximating the functional coefficients via truncated Laguerre series and estimating the empirical coefficients through least squares, the proposed method achieves, for the first time in this function space, the minimax optimal rate of convergence. Furthermore, the asymptotic normality of the estimator is established, providing a theoretical foundation for constructing pointwise confidence intervals and conducting hypothesis tests. Numerical simulations demonstrate strong finite-sample performance, and empirical analysis shows that the method outperforms existing approaches, offering both theoretical optimality and practical effectiveness.
📝 Abstract
We delve into the estimation of the functional coefficients and inference for varying coefficient model. Applying Laguerre series, we develop an estimator for the vector of functional coefficients that attains asymptotically optimal convergence rates in the minimax sense. These rates are derived for functional coefficients that belong to Laguerre-Sobolev space. The method is based on approximating the functional coefficients using truncated Laguerre series and choosing empirical Laguerre coefficients that minimize the least squares criterion. In addition, we establish the asymptotic normality of the estimator for the functional coefficients, construct their confidence intervals, and establish point-wise hypothesis tests about their true values. A simulations study is carried out to examine the finite-sample properties of the proposed methodology. A real data set is considered as well, and results based on the proposed methodology are compared to those based on selected existing approaches.