We review different approaches to nonparametric density and regression estimation. Kernel
estimators are motivated from local averaging and solving ill-posed problems. Kernel …

This book concerns the problem of data smoothing. There are many smoothing techniques,
yet the kernel smoothing seems to be one of the most important and widely used ones. In …

Nonparametric methods play a central role in modern empirical work. While they provide
inference procedures that are more robust to parametric misspecification bias, they may be …

Kernel smoothing has greatly evolved since its inception to become an essential
methodology in the data science tool kit for the 21st century. Its widespread adoption is due …

The existence of high speed, inexpensive computing has made it easy to look at data in
ways that were once impossible. Where once a data analyst was forced to make restrictive …

If a probability density function has bounded support, kernel density estimates often overspill
the boundaries and are consequently especially biased at and near these edges. In this …

This paper develops a nonparametric density estimator with parametric overtones. Suppose
f (x, θ) is some family of densities, indexed by a vector of parameters θ. We define a local …

A new method for bias reduction in nonparametric density estimation is proposed. The
method is a simple, two-stage multiplicative bias correction. Its theoretical properties are …

We explore the aims of, and relationships between, various kernel-type regression
estimators. To do so, we identify two general types of (direct) kernel estimators differing in …

We consider many kernel-based density estimators, all theoretically improving bias from O
(h 2), as the smoothing parameter h→ 0, to O (h 4). Examples include higher-order kernels …