John Braun

Differential Equation-Assisted Local Polynomial Regression

Local polynomial regression is a popular technique for smoothing a scatterplot of data.  Use of higher-order local polynomial regression is often problematic in cases of data sparsity (which might be a result of data missing at random, for example), and it is also prone to variance inflation. Although local constant regression is usable when data are sparse, the results can be misleading, due to increased bias, particularly at the data boundaries.  If the underlying regression function is assumed to satisfy or approximately satisfy a differential equation, a procedure with similar variance properties to local constant regression can be employed, leading to noticeable decreases in bias.