VARIABLE KERNEL DENSITY ESTIMATES AND VARIABLE KERNEL DENSITY ESTIMATES

Summary The term “variable kernel density estimate” is sometimes used to mean a kernel density estimate employing a different bandwidth for each data point, and sometimes to denote a kernel density estimate with bandwidth a function of estimation location. This expository article stresses the importance of the distinction between these two definitions, both via an introductory description of the ideas involved and in terms of their comparative theoretical performance.