Let fn denote a kernel density estimator of a density f on the real line, for a bounded, compactly supported probability kernel. Under relatively weak smoothness conditions on f and K it is proved, for every 0 < β < 1/2, that the sequence Ân ( √ nhn ‖K‖2‖fn‖ ∞ sup t∈D̂an |fn(t) − f(t)| f n (t) − Ân ) converges in distribution to the double exponential law. Here Ân is constructed from the sample,...

In this paper we investigate the problem of estimating density for continuous time processes when continuous sampling is available. Consider an R-valued stochastic process (Xt, t ∈ R) such that each Xt has the same distribution, say μ, with unknown density, say f . In the following we construct the kernel density estimator fT based upon the data (Xt, 0 ≤ t ≤ T ) and study its asymptotic behavio...

This paper deals with the asymptotic properties of the Metropolis-Hastings algorithm, when the distribution of interest is unknown, but can be approximated by a sequential estimator of its density. We prove that, under very simple conditions, the rate of convergence of the Metropolis-Hastings algorithm is the same as that of the sequential estimator when the latter is introduced as the reversib...

We propose a local linear estimator of a smooth distribution function. This estimator applies local linear techniques to observations from a regression model in which the value of the empirical distribution function equals the value of true distribution plus an error term. We show that, for most commonly used kernel functions, our local linear estimator has a smaller asymptotic mean integrated ...

This paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms. Based on the …xed-bandwidth asymptotic variance and the pre-asymptotic variance, we propose a heteroskedasticity and autocorrelation robust (HAR) variance estimator that achieves double robustness — it is asymptotically valid regardless of whether the temporal ...

for an unknown vector of parameters β0 and an unknown univariate function τ(·). This model is implied by many important limited dependent variable and regression models, as discussed in Ruud (1986) and Stoker (1986). Consistent estimators for β0, up to an unknown scale factor, have been developed by Ruud (1986), Stoker (1986), Powell, Stock, and Stoker (1989), Ichimura (1993), and others. In th...

Iowa State University, The University of Western Australia and Iowa State University We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a studentized L2-distance between the kernel t...

A simple and effective object recognition scheme is to represent and match images on the basis of color histograms. To obtain robustness against varying imaging circumstances (e.g. a change in illumination, object pose, and viewpoint), color histograms are constructed from color invariants. However, in general, color invariants are negatively affected by sensor noise due to the instabilities of...

Density estimates based on point processes are often restrained to regions with irregular boundaries or holes. We propose a density estimator, the lattice-based density estimator, which produces reasonable density estimates under these circumstances. The estimation process starts with overlaying the region with nodes, linking these together in a lattice and then computing the density of random ...