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Nonparametric Regression. -m(x) is a general function that relates x to y. This specification includes the linear regression model as a special case. -Now we must estimate a function rather than just two parameters. -Nonparametric: No parameters. Nonparametric Regression.

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nonparametric regression
Nonparametric Regression

-m(x) is a general function that relates x to y. This specification includes the linear regression model as a special case.

-Now we must estimate a function rather than just two parameters.

-Nonparametric: No parameters.

nonparametric regression1
Nonparametric Regression
  • There are a variety of techniques for estimating these functions. One popular method is the local polynomial regression estimator:
  • This seems rather complicated?
nonparametric regression2
Nonparametric Regression
  • It turns out that this “intuitive method” is a special case of the general procedure:
  • We can make improvements by estimating the function over a fine grid and assigning weights to the data points within the shaded region.