Bivariate Penalized Splines for Regression
نویسندگان
چکیده
In this paper the asymptotic behavior of penalized spline estimators is studied using bivariate splines over triangulations and an energy functional as the penalty. The rate of L2 convergence is derived, which achieves the optimal nonparametric convergence rate established by Stone (1982). The asymptotic normality of the penalized spline estimators is established, which is shown to hold uniformly over the points where the regression function is estimated. The size of the asymptotic conditional variance is also evaluated and a simple expression for the asymptotic variance is given. Simulation experiments have provided strong evidence that corroborates with the asymptotic theory.
منابع مشابه
Nonparametric M-quantile Regression via Penalized Splines
Quantile regression investigates the conditional quantile functions of a response variables in terms of a set of covariates. Mquantile regression extends this idea by a “quantile-like” generalization of regression based on influence functions. In this work we extend it to nonparametric regression, in the sense that the M-quantile regression functions do not have to be assumed to be linear, but ...
متن کاملOn Semiparametric Regression with O'sullivan Penalized Splines
An exposition on the use of O’Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented. O’Sullivan penalized splines are similar to P-splines, but have the advantage of being a direct generalization of smoothing splines. Exact expressions for the O’Sullivan penalty matrix are obtained. Comparisons between the two types o...
متن کاملSpline Estimator for the Functional Linear Regression with Functional Response
The article is devoted to a regression setting where both, the response and the predictor, are random functions defined on some compact sets of R. We consider functional linear (auto)regression and we face the estimation of a bivariate functional parameter. Conditions for existence and uniqueness of the parameter are given and an estimator based on a B-splines expansion is proposed using the pe...
متن کاملExploring US Business Cycles with Bivariate Loops using Penalized Spline Regression
The phrase business cycle is usually used for short term fluctuations in macroeconomic time series. In this paper we focus on the estimation of business cycles in a bivariate manner by fitting two series simultaneously. The underlying model is thereby nonparametric in that no functional form is prespecified but smoothness of the functions are assumed. The functions are then estimated using pena...
متن کامل