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...

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...

To cite: Matsumoto N, Suzuki Y, Yoda S, et al. BMJ Case Rep Published online: [please include Day Month Year] doi:10.1136/bcr-2014205407 DESCRIPTION Recognition of the truncation artefact is important for the control of image quality on myocardial perfusion images in single-photon emission CT (SPECT). Truncation artefact is usually seen in obese patients who may deviate from a γ-ray detector fi...

In many applications, the available data come from a sampling scheme that causes loss of information in terms of left truncation. In some cases, in addition to left truncation, the data are weakly dependent. In this paper we are interested in deriving the asymptotic normality as well as a Berry-Esseen type bound for the kernel density estimator of left truncated and weakly dependent data.

Survival data collected from a prevalent cohort are subject to left truncation and the analysis is challenging. Conditional approaches for left-truncated data could be inefficient as they ignore the information in the marginal likelihood of the truncation times. Length-biased sampling methods may improve the estimation efficiency but only when the underlying truncation time is uniform; otherwis...

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...

The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for ...

the purpose of this paper is to provide some asymptotic results for nonparametric estimator of the lorenz curve and lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. first, we show that nonparametric estimator of the lorenz curve is uniformly strongly consistent for the associated lorenz curve. also, a strong gaussian approximation for ...