Nonparametric estimation of piecewise smooth regression functions

نویسنده

  • Michael Kohler
چکیده

Estimation of univariate regression functions from bounded i.i.d. data is considered. Estimates are deened by minimizing a complexity penalized residual sum of squares over all piecewise polynomials. The integrated squared error of these estimates achieves for piecewise p-smooth regression functions the rate (ln 2 (n)=n) 2p 2p+1 .

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Estimation of Piecewise-smooth Functions by Amalgamated Bridge Regression Splines

We consider nonparametric estimation of a one-dimensional piecewise-smooth function observed with white Gaussian noise on an interval. We propose a two-step estimation procedure, where one first detects jump points by a wavelet-based procedure and then estimates the function on each smooth segment separately by bridge regression splines. We prove the asymptotic optimality (in the minimax sense)...

متن کامل

Asymptotically Minimax Estimation of a Function with Jumps

Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L 2-loss function. The unknown function f is assumed to be m times diierentiable except for an unknown, though nite, number of jumps, with piecewise mth derivative bounded in L 2-norm. An estimator is constructed, attaining the same o...

متن کامل

A New Nonparametric Regression for Longitudinal Data

In many area of medical research, a relation analysis between one response variable and some explanatory variables is desirable. Regression is the most common tool in this situation. If we have some assumptions for such normality for response variable, we could use it. In this paper we propose a nonparametric regression that does not have normality assumption for response variable and we focus ...

متن کامل

Detecting Abrupt Changes by Wavelet Methods

The objective of this paper is to contribute to the methodology available for dealing with the detection and the estimation of the location of discontinuities in one dimensional piecewise smooth regression functions observed in white Gaussian noise over an interval. Our approach is nonparametric in nature because the unknown function is not assumed to have any speciic form. Our method relies up...

متن کامل

Shape constrained estimation using nonnegative splines

We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support, using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal s...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1998