sample values are chosen. Equations (51) and (58) are derived [14] T. Lyche and L. L. Schumaker, " Computation of smoothing and in a similar fashion. interpolating natural splines via local bases, " SIAM J.

The asymptotic behaviour of penalized spline estimators is studied in the univariate case. We use B -splines and a penalty is placed on mth-order differences of the coefficients. The number of knots is assumed to converge to infinity as the sample size increases. We show that penalized splines behave similarly to Nadaraya-Watson kernel estimators with ‘equivalent’ kernels depending upon m. The ...