Asymptotics for penalized splines in generalized additive models
  This paper discusses asymptotic theory for penalized spline estimators in generalized additive models. The purpose of this paper is to establish the asymptotic bias and variance as well as the asymptotic normality of the penalized spline estimators proposed by Marx and Eilers (1998). Furthermore, the asymptotics for the penalized quasi likelihood fit in mixed models are also discussed. 
Takuma Yoshida and Kanta Naito
math.ST stat.TH