Simple Kernel Estimators for
نویسنده
چکیده
We consider deconvolution problems where the observations are equal in distribution to Here the random variables in the sums are independent, the E i are exponentially distributed, the L i are Laplace distributed and Y has an unknown distribution F which we want to estimate. The constants i or i are given. These problems include exponential, gamma and Laplace deconvolution. We derive inversion formulas, expressing F in terms of the distribution of the observations. Simple kernel estimators are then introduced by plugging in standard kernel estimators of the distribution of the observations. The pointwise asymptotic properties of the estimators are investigated.
منابع مشابه
Density Estimators for Truncated Dependent Data
In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...
متن کاملAsymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data
Kernel density estimators are the basic tools for density estimation in non-parametric statistics. The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in which the bandwidth is varied depending on the location of the sample points. In this paper, we initially introduce the k-nearest neighbor kernel density estimator in the random left-truncatio...
متن کاملComparison of the Gamma kernel and the orthogonal series methods of density estimation
The standard kernel density estimator suffers from a boundary bias issue for probability density function of distributions on the positive real line. The Gamma kernel estimators and orthogonal series estimators are two alternatives which are free of boundary bias. In this paper, a simulation study is conducted to compare small-sample performance of the Gamma kernel estimators and the orthog...
متن کاملAggregating Density Estimators: An Empirical Study
Density estimation methods based on aggregating several estimators are described and compared over several simulation models. We show that aggregation gives rise in general to better estimators than simple methods like histograms or kernel density estimators. We suggest three new simple algorithms which aggregate histograms and compare very well to all the existing methods.
متن کاملNon-parametric adaptive estimation of a multivariate density ?
The properties of adaptive non-parametric kernel estimators for the multivariate probability density f(x) (and its derivatives) of identically distributed random vectors εn, n ≥ 1 at a given point are studied. It is supposed that the vectors εn, n ≥ 1 form a martingaledifference process (εn)n≥1 and the function to be estimated belongs to a class of densities slightly narrower than the class of ...
متن کامل