Kapil Sharma

I previously wrote a post about Kernel Smoothing and how it can be used to fit a non-linear function non-parametrically. In this post, I will extend on that idea and try to mitigate the disadvantages of kernel smoothing using Local Linear Regression. I generated some data in my previous post and I will reuse the same data for this post. The data was generated from the function $\mathbf{y f(x) sin(4x) 2}$ with some Gaussian noise and here's how it looks: As I mentioned in the previous article, in kernel smoothing out-of-sample predictions on the edges and in sparse regions can have significant errors and bias. In Local Linear Regression, we try to reduce this bias to first order, by fitting straight lines instead of local constants.