ABSTRACT
This chapter develops variable bandwidth estimators which apply varying amounts of smoothing to tackle heavy-tailed data. It presents transformation and boundary kernel estimators to tackle bounded data. The chapter examines the role of the kernel function and the alternatives to the normal kernel. It provides the mathematical details of the considered modified density estimators. The first class of variable density estimators is the balloon density estimators where the bandwidth varies with the estimation point. Another type of variable kernel estimator is the sample point estimator, where a different bandwidth is employed to rescale the kernel around each data point. Transformation estimators apply a transformation function which implicitly modifies the kernel function in order to reduce the bias in the boundary region, an alternative approach involves explicitly modifying the kernel functions in the boundary region from the usual symmetric to asymmetric functions to account for the rigid boundary.
