Results 1  10
of
10
A DesignAdaptive Local Polynomial Estimator for the ErrorsinVariables Problem
"... Abstract: Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errorsinvariables context by exploiting its similarity with ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
Abstract: Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errorsinvariables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however, is not straightforward and has remained an open problem for the last 15 years, since the publication of Fan and Truong (1993). We propose an innovative local polynomial estimator of any order in the errorsinvariables context, derive its designadaptive asymptotic properties and study its finite sample performance on simulated examples. We provide not only a solution to a longstanding open problem, but also provide methodological contributions to errorinvariable regression, including local polynomial estimation of derivative functions.
Deconvolution for an atomic distribution
, 2008
"... Let X1,..., Xn be i.i.d. observations, where Xi = Yi + σZi and Yi and Zi are independent. Assume that unobservable Y ’s are distributed as a random variable UV, where U and V are independent, U has a Bernoulli distribution with probability of zero equal to p and V has a distribution function F with ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
Let X1,..., Xn be i.i.d. observations, where Xi = Yi + σZi and Yi and Zi are independent. Assume that unobservable Y ’s are distributed as a random variable UV, where U and V are independent, U has a Bernoulli distribution with probability of zero equal to p and V has a distribution function F with density f. Furthermore, let the random variables Zi have the standard normal distribution and let σ> 0. Based on a sample X1,..., Xn, we consider the problem of estimation of the density f and the probability p. We propose a kernel type deconvolution estimator for f and derive its asymptotic normality at a fixed point. A consistent estimator for p is given as well. Our results demonstrate that our estimator behaves very much like the kernel type deconvolution estimator in the classical deconvolution problem.
The effects of error magnitude and bandwidth selection for deconvolution with unknown error distribution
 J NONPARAMETRIC STAT
"... ..."
Bert van Es Kortewegde Vries Instituut voor Wiskunde
, 2008
"... Some thoughts on the asymptotics of the deconvolution kernel density estimator ..."
Abstract
 Add to MetaCart
Some thoughts on the asymptotics of the deconvolution kernel density estimator
unknown title
, 2009
"... Asymptotic normality of the deconvolution kernel density estimator under the vanishing error variance ..."
Abstract
 Add to MetaCart
Asymptotic normality of the deconvolution kernel density estimator under the vanishing error variance
unknown title
, 2009
"... Asymptotic normality of the deconvolution kernel density estimator under the vanishing error variance ..."
Abstract
 Add to MetaCart
Asymptotic normality of the deconvolution kernel density estimator under the vanishing error variance
Submitted to the Annals of Applied Statistics arXiv: math.PR/0000000 SCANNING A POISSON RANDOM FIELD FOR LOCAL SIGNALS
"... The detection of local genomic signals using highthroughput DNA sequencing data can be cast as a problem of scanning a Poisson random field for local changes in the rate of the process. We propose a likelihoodbased framework for for such scans, and derive formulas for false positive rate control a ..."
Abstract
 Add to MetaCart
The detection of local genomic signals using highthroughput DNA sequencing data can be cast as a problem of scanning a Poisson random field for local changes in the rate of the process. We propose a likelihoodbased framework for for such scans, and derive formulas for false positive rate control and power calculations. The framework can also accommodate mixtures of Poisson processes to deal with overdispersion. As a specific, detailed example, we consider the detection of insertions and deletions by pairedend DNAsequencing. We propose several statistics for this problem, compare their power under current experimental designs, and illustrate their application on an Illumina Platinum Genomes data set. 1. Introduction. Modern biology
Misclassification Rates in Hypertension Diagnosis due to Measurement Errors
"... Abstract. Using a mixture of two normal distributions, we estimate the false positive and false negative errors in the diagnosis of hypertension. Parameters in the mixture are estimated by the expectationmaximization (EM) algorithm. It is shown that both errors depend on cutoff points. Repeated mea ..."
Abstract
 Add to MetaCart
Abstract. Using a mixture of two normal distributions, we estimate the false positive and false negative errors in the diagnosis of hypertension. Parameters in the mixture are estimated by the expectationmaximization (EM) algorithm. It is shown that both errors depend on cutoff points. Repeated measurements reduce both errors dramatically. The number of repeated measurements is recommended through a simulation study. 1
Deconvolution in Nonparametric Statistics
"... Abstract. In this tutorial paper we give an overview of deconvolution problems in nonparametric statistics. First, we consider the problem of density estimation given a contaminated sample. We illustrate that the classical RosenblattParzen kernel density estimator is unable to capture the full shap ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. In this tutorial paper we give an overview of deconvolution problems in nonparametric statistics. First, we consider the problem of density estimation given a contaminated sample. We illustrate that the classical RosenblattParzen kernel density estimator is unable to capture the full shape of the density while the presented method experiences almost no problems. Second, we use the previous estimator in a nonparametric regression framework with errorsinvariables. 1