Abstract
The Receiver Operating Characteristic (ROC) curve is a statistical tool for evaluating the accuracy of diagnostics tests. The empirical ROC curve (which is a step function) is the most commonly used non-parametric estimator for the ROC curve. On the other hand, kernel smoothing methods have been used to obtain smooth ROC curves. The preceding process is based on kernel estimates of the distribution functions. It has been observedthat kernel distribution estimators are not consistent when estimating a distribution function near the boundary of its support. This problem is due to “boundary effects” that occur in nonparametric functional estimation. To avoid these difficulties, we propose a generalized reflection method of boundary correction in the estimation problem of ROC curves. The proposed method generates a class of boundary corrected estimators.
Highlights
The Receiver Operating Characteristic (ROC) describes the performance of a diagnostic test which classifies subjects into either group without condition G0 or group with condition G1 by means of a continuous discriminant score X, i.e., a subject is classified as G1 if X ≥ d and G0 otherwise for a given cutoff point d ∈ R
From expression (1) it is clear that the bias of Fh,K(x) is of order O(h) instead of O(h2). To remove this boundary effect in kernel distribution estimation we investigate a new class of estimators
In this paper we proposed a new kernel-type distribution estimator to avoid the difficulties near the boundary
Summary
The Receiver Operating Characteristic (ROC) describes the performance of a diagnostic test which classifies subjects into either group without condition G0 or group with condition G1 by means of a continuous discriminant score X, i.e., a subject is classified as G1 if X ≥ d and G0 otherwise for a given cutoff point d ∈ R. A simple non-parametric estimator for R(p) is to use the empirical distribution functions for F0 and F1. The resulting ROC curve is a step function and it is called the empirical ROC curve. Another type of non-parametric estimator for R(p) is derived from kernel smoothing methods. Applications of kernel smoothing in distribution function estimation are relatively few. Some theoretical properties of a kernel distribution function estimator have been investigated by Nadaraya (1964), Reiss (1981), and Azzalini (1981). Lloyd (1998) proposed a nonparametric estimator of ROC by using kernel estimators for the distribution functions F0 and F1 Some theoretical properties of a kernel distribution function estimator have been investigated by Nadaraya (1964), Reiss (1981), and Azzalini (1981). Lloyd (1998) proposed a nonparametric estimator of ROC by using kernel estimators for the distribution functions F0 and F1
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