We consider the problem of estimating a probability density function based on data that are corrupted by noise from a uniform distribution. The (nonparametric) maximum likelihood estimator for the corresponding distribution function is well defined. For the density function this is not the case. We study two nonparametric estimators for this density. The first is a type of kernel density estima...

This paper studies probability density estimation on the Siegel space. The Siegel space is a generalization of the hyperbolic space. Its Riemannian metric provides an interesting structure to the Toeplitz block Toeplitz matrices that appear in the covariance estimation of radar signals. The main techniques of probability density estimation on Riemannian manifolds are reviewed. For computational...

A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multiple taper estimate. This procedure reduces the expected mean square error by (π 2 4) 4/5 over simply smoothing the log tapered periodogram. A data adaptive implementation of a variable bandwidth kernel smoother is given.

Kernel density estimation is an important technique for understanding the distributional properties of data. Some investigations have found that the estimation of a global bandwidth can be heavily affected by observations in the tail. We propose to categorize data into lowand high-density regions, to which we assign two different bandwidths called the low-density adaptive bandwidths. We derive ...

This paper considers the asymptotic distributions of the error density estimators in first-order autoregressive models. At a fixed point, the distribution of the error density estimator is shown to be normal. Globally, the asymptotic distribution of the maximum of a suitably normalized deviation of the density estimator from the expectation of the kernel error density (based on the true error) ...

We propose to approximate the unknown error density of a nonparametric regression model by a mixture of Gaussian densities with means being the individual error realizations and variance a constant parameter. This mixture density has the form of a kernel density estimator of error realizations. We derive an approximate likelihood and posterior for bandwidth parameters in the kernel–form error d...

We derive an approximation of a density estimator based on weakly dependent random vectors by a density estimator built from independent random vectors We construct on a su ciently rich probability space such a pairing of the random variables of both experiments that the set of observations fX Xng from the time series model is nearly the same as the set of observations fY Yng from the i i d mod...

The asymptotically best bandwidth selectors for a kernel density estimator currently require the use of either unappealing higher order kernel pilot estimators or related Fourier transform methods. The point of this paper is to present a methodology which allows the fastest possible rate of convergence with the use of only nonnegative kernel estimators at all stages of the selection process. Th...

We consider discrete time models for asset prices with a stationary volatility process. We aim at estimating the multivariate density of this process at a set of consecutive time instants. A Fourier type deconvolution kernel density estimator based on the logarithm of the squared process is proposed to estimate the volatility density. Expansions of the bias and bounds on the variance are derived.

In statistics, the univariate kernel density estimation (KDE) is a non-parametric way to estimate the probability density function f(x) of a random variable X, is a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. This techniques are widely used in various inference procedures such as signal processing, data mining and econometric...