Asymptotic properties of penalized spline estimators in concave extended linear models: Rates of convergence

This paper develops a general theory on rates of convergence penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where interpreted broad sense that includes conditional likelihood, quasi-likelihood and pseudo-likelihood. The allows all feasible combinations degree, penalty order smoothness unknown functions. According to this theory, asymptotic behaviors depends interplay between knot number parameter. applied obtain results variety contexts, including regression, generalized regression such as logistic Poisson density estimation, hazard censored data, quantile diffusion type process spectral stationary time series. For multidimensional (presented Supplementary Material) covers both tensor product splines bivariate triangulations.