Asymptotics of Penalized spline estimations

  Yingxing (Amy) Li
  Cornell University

The asymptotic behavior of penalized spline estimators is studied 
both in the univariate and multivariate case. We use B-splines 
and a penalty is placed on the m-th order differences of the 
coefficients. The number of knots are assumed to converge to infinity 
faster than a minimum bound as the sample size increases and the 
penalty parameter plays the role of smoothing. We show that penalized 
splines behave similarly to Nadaraya-Watson kernel estimators. The 
asymptotic distribution is Gaussian and the expressions for the 
asymptotic mean and variance are given.