Transcription of Lecture 12 Nonparametric Regression
{{id}} {{{paragraph}}}
Example: marketing
Lecture 12 Nonparametric Regression
RS EC2 - Lecture 1111 Lecture 12 Nonparametric Regression The goal of a Regression analysis is to produce a reasonable analysis to the unknown response function f, where for Ndata points (Xi,Yi), the relationship can be modeled as - Note: m(.) = E[y|x]if E[ |x]=0 , x We have different ways to model the conditional expectation function (CEF), m(.):-Parametric approach- Nonparametric approach- Semi-parametric Parametric Regression : IntroductionNixmyiii,,1,)( RS EC2 - Lecture 112 Parametric approach: m(.) is known and smooth. It is fully described by a finite set of parameters, to be estimated. Easy interpretation. For example, a linear model: Nonparametric approach: m(.) is smooth, flexible, but unknown. Let the data determine the shape of m(.). Difficult interpretation. Semi-parametric approach: m(.) have some parameters -to be estimated-, but some parts are determined by the Parametric Regression : IntroductionNixyiii,,1,' Nixmyiii,,1,)( Nizmxyiizii,,1,)(' 4 Non Parametric Regression : IntroductionRS EC2 - Lecture 1135 Regression : Smoothing We want to relate y with x, without assuming any functional form.
That is, a kernel regression estimator is a local constant regression, since it sets m(x) equal to a constant, θ, in the very small neighborhood of x0: Note: The residuals are weighted quadratically => weighted LS! ... using the density estimation results.
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: