Consider a partial linear model, where the expectation of a random variable Y depends on covariates $(x, z)$ through $F(\theta_0 x + m_0(z))$, with $\theta_0$ an unknown parameter, and $m_0$ an unknown function. We apply the theory of empirical processes to derive the asymptotic properties of the penalized quasi-likelihood estimator.
"Penalized quasi-likelihood estimation in partial linear models." Ann. Statist. 25 (3) 1014 - 1035, June 1997. https://doi.org/10.1214/aos/1069362736