Standard kernel density estimation methods are very often used in practice to estimate density function. It works well in numerous cases. However, it is known not to work so well with skewed, multimodal and heavy-tailed distributions. Such features are usual with income distributions, defined...

The recent priority given to Federal Crop Insurance as an agricultural policy instrument has increased the importance of rate making procedures. Actuarial soundness requires rates that are actuarially fair: the premium is set equal to expected loss. Formation of this expectation depends, in the...

We develop a nonparametric estimator of the stochastic volatility density of a discretely-observed Ito semimartingale in the setting of an increasing time span and finer mesh of the observation grid. There are two steps. The first is aggregating the high-frequency increments into the realized...

We provide a new perspective on disagreement in inflation expectations by examining the full probability distributions of UK consumer inflation forecasts based on an adaptive bootstrap multimodality test. Furthermore, we compare the inflation forecasts of the Bank of England's Monetary Policy...

Least squares cross-validation (CV) methods are often used for automated bandwidth selection. We show that they share a common structure which has an explicit asymptotic solution that we derive. Using the framework of density estimation, we consider unbiased, biased, and smoothed CV methods. We...

In this paper, a method for estimating monotone, convex and log-concave densities is proposed. The estimation procedure consists of an unconstrained kernel estimator which is modi?ed in a second step with respect to the desired shape constraint by using monotone rearrangements. It is shown that...