In the random sampling setting we estimate the entropy of a probability density distribution by the entropy of a kernel density estimator using the double exponential kernel. Under mild smoothness and moment conditions we show that the entropy of the kernel density estimator equals a sum of independent and identically distributed (i.i.d.) random variables plus a perturbation which is asymptotic...

Abstract We propose a new method to estimate the empirical pricing kernel based on option data. We estimate the pricing kernel nonparametrically by using the ratio of the risk-neutral density estimator and the subjective density estimator. The risk-neutral density is approximated by a weighted kernel density estimator with varying unknown weights for different observations, and the subjective d...

Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic properties of this estimator depend on the average prediction error of the functional autoregressive function. Sufficient conditions are studied to provide stro...

Suppose we have independent observations of a pair of independent random variables, one with a density and the other discrete. The sum of these random variables has a density, which can be estimated by an ordinary kernel estimator. Since the two components are independent, we can write the density as a convolution and alternatively estimate it by a convolution of a kernel estimator of the conti...

We consider finite-order moving average and nonlinear autoregressive processes with no parametric assumption on the error distribution, and present a kernel density estimator of a bootstrap series that estimates their marginal densities root-n consistently. This is equal to the rate of the best known convolution estimators, and faster than the standard kernel density estimator. We also conduct ...

A modification of the kernel estimator for density estimation is proposed which allows the incorporation of local information about the smoothness of the density. The estimator uses a small set of bandwidths rather than a single global one as in the standard kernel estimator. It uses a set of filtering functions which determine the extent of influence of the individual bandwidths. Various versi...