Skip to Main Content
Kernel Smoothing
book

Kernel Smoothing

by Sucharita Ghosh
January 2018
Intermediate to advanced content levelIntermediate to advanced
272 pages
5h 48m
English
Wiley
Content preview from Kernel Smoothing

2Nonparametric Regression

2.1 Introduction

Consider the bivariate random variable where X denotes an explanatory variable and Y denotes the response or the dependent variable. Consider the observations

(2.1)numbered Display Equation

on the pair (X, Y). Although in this discussion, we let X be a scalar, the ideas presented here can easily be generalized to the multidimensional case, i.e., when . Similarly, the response variable Y is in , though multivariate regression is also possible to consider. Moreover, let Y be continuous and in the sequel we will impose some further moment conditions. Nonparametric regression is concerned with the situation when the regression function, i.e., the conditional expected value of Y given X has an arbitrary shape, apart from satisfying some smoothness conditions.

Specifically, our interest lies in estimating the function m, which is the nonparametric regression function

(2.2)numbered Display Equation

where denotes the conditional expectation of Y given X = x. For simplicity of notation, we write ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Smoothing Splines

Smoothing Splines

Yuedong Wang
Handbook of Discrete-Valued Time Series

Handbook of Discrete-Valued Time Series

Richard A. Davis, Scott H. Holan, Robert Lund, Nalini Ravishanker

Publisher Resources

ISBN: 9781118456057Purchase book