Smoothing Spline Estimation in Varying-Coefficient Models

Abstract

Smoothing spline estimators are considered for inference in varying-coefficient models with one effect modifying covariate. Bayesian 'confidence intervals' are developed for the coefficient curves and efficient computational methods are derived for computing the curve estimators, fitted values, posterior variances and data-adaptive methods for selecting the levels of smoothing. The efficacy and utility of the methodology proposed are demonstrated through a small simulation study and the analysis of a real data set. Copyright 2004 Royal Statistical Society.

Reducing component estimation for varying coefficient models with longitudinal data

“…However, the component-based methods, although adequate for time-invariant covariates, are not applicable when some of the covariates are timedependent. In [10] ε i (t ij ) is assumed to be uncorrelated and in [11] two-step procedure is mainly used for regularly placed observation times and the asymptotic variances of the estimators are studied in the case that the covariates are time-invariant. The asymptotic properties of the estimators in [12] are derived only in the case that the covariates X(t) are bounded.…”

“…Since the local polynomial method involves only one smoothing parameter, it often undersmooths some of the underlying coefficient functions when these coefficient functions admit different degrees of smoothness. To introduce different amounts of smoothing for different coefficient functions, [2,9] proposed a component-based kernel and smoothing spline estimates; [10] developed an effective computational method to compute the smoothing spline estimators of β(t); [11] suggested a two-step estimation and [12] proposed the method based on function approximation through basis expansions. However, the component-based methods, although adequate for time-invariant covariates, are not applicable when some of the covariates are timedependent.…”

Modelling inflation in transportation, comunication and financial services using B-Spline time series model

“…The shape is quite complex but does not require assumptions. Nonparametric approach is a model estimation method based on unconstrained approach of assumption of certain regression curve form where the regression curve is assumed only smooth, meaning it is contained in a certain function room so that nonparametric regression has high flexibility because the regression curve estimation form adjusts its data without being influenced by the research subjectivity factor [4]. The basic assumption of nonparametric regression is the presence of a smoothing that links the y response variable to one or more predictor variables x. Regression nonparametric model with observation (x i, y i ) ; as follow as: …”

“…The concept of nonparametric regression modeling is the estimation curve looking for its own form of function against the distribution of data, so the modeling is not dependent on the parameters, but the parameters are generated from the approximate data pattern [3]. A nonparametric regression approach has been widely used, among others Spline [4], Local Polynomial, Wavelet, Fourier, Neural Network. Regression method is usually used for cross section data, but regression method can be developed for time series data modeling.…”

Fast Function-on-Scalar Regression with Penalized Basis Expansions

“…On the one hand, roughness penalization allows for the use of a rich basis, as opposed to unpenalized spline approaches ) that may require a careful choice of a limited number of knots. On the other hand, low-rank spline bases may offer substantial computational savings over smoothing splines with a knot at each observation point, even when the latter are efficiently implemented as in Eubank et al (2004).…”