Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves

We propose a framework for estimation of the conditional mean function in a parametric model with function space covariates. The approach employs a functional mean squared error objective criterion. Under regularity conditions, consistency and asymptotic normality are established. The analysis extends to situations where the asymptotic properties are influenced by estimation errors arising from the presence of nuisance parameters. Wald, Lagrange multiplier, and quasi‐likelihood ratio statistics are studied. An empirical application conducts lifetime income path comparisons across different demographic groups according to years of work experience.