Abstract: This paper performs an asymptotic analysis of penalized spline estimators. We compare P -splines and splines with a penalty of the type used with smoothing splines. The asymptotic rates of the supremum norm of the difference between these two estimators over compact subsets of the interior and over the entire interval are established. It is shown that a Pspline and a smoothing spline ...

in this paper, an adaptive physics-based method is developed for solving wave motion problems in one dimension (i.e., wave propagation in strings, rods and beams). the solution of the problem includes two main parts. in the first part, after discretization of the domain, a physics-based method is developed considering the conservation of mass and the balance of momentum. in the second part, ada...

There is a well-known Bayesian interpretation for function estimation by spline smoothing using a limit of proper normal priors. The limiting prior and the conditional and intrinsic autoregressive priors popular for spatial modelling have a common form, which we call partially informative normal. We derive necessary and sufficient conditions for the propriety of the posterior for this class of ...

The Hybrid Spline method (H-spline) is a method of density estimation which involves regression splines and smoothing splines methods. Using basis functions (B-splines), this method is much faster than Smoothing Spline Density Estimation approach (Gu, 1993). Simulations suggest that with more structured data (e.g., several modes) H-spline method estimates the modes as well as Logspline (Kooperb...

We first consider a Bayesian formalism in the wavelet domain that gives rise to the regularised linear wavelet estimator obtained in the standard nonparametric regression setting when the unknown response function belongs to a Sobolev space with non-integer regularity s > 1/2. We then use the posterior distribution of the wavelets coefficients to construct pointwise Bayesian credible intervals ...

In this paper we give a basic derivation of smoothing and interpolating splines and through this derivation we show that the basic spline construction can be done through elementary Hilbert space techniques. Smoothing splines are shown to naturally separate into a filtering problem on the raw data and an interpolating spline construction. Both the filtering algorithm and the interpolating splin...

BACKGROUND AND OBJECTIVE Cox model is a popular model in survival analysis, which assumes linearity of the covariate on the log hazard function, While continuous covariates can affect the hazard through more complicated nonlinear functional forms and therefore, Cox models with continuous covariates are prone to misspecification due to not fitting the correct functional form for continuous covar...

We present a novel smoothing approach to nonparametric regression curve fitting. This is based on kernel partial least squares (PLS) regression in reproducing kernel Hilbert space. It is our interest to apply the methodology for smoothing experimental data, such as brain event related potentials, where some level of knowledge about areas of different degrees of smoothness, local inhomogeneities...