Polynomial and special function theory remains a vibrant area of mathematical research, interweaving classical algebra with advanced analysis. At its core, the study concerns algebraic expressions ...

The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focused on local polynomial smoothers.

Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions ...