# Estimating the Local Mean Function

Estimating the Local Mean Function

The linear regression model =m+b+σ relies on a number of crucial assumptions, the most important of which is a linear relationship between the covariate and the dependent variable . One way of generalizing the standard linear regression model is to extend it to the nonlinear form =m()+σ(), where and are real-valued functions and is an independent, identically distributed sequence of standard normal random variables. We study five different sets of data (three "real" and two simulated) to illustrate how kernel-weighted least-squares regression can be used to estimate the local mean function .

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m(x)=E[|=x]

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