Abstract
Abstract Consider a survival time study, where a sequence of possibly censored failure times is observed with d-dimensional covariate The main goal of this article is to establish the asymptotic normality of the kernel estimator of the relative error regression function when the data exhibit some kind of dependency. The asymptotic variance is explicitly given. Some simulations are drawn to lend further support to our theoretical result and illustrate the good accuracy of the studied method. Furthermore, a real data example is treated to show the good quality of the prediction and that the true data are well inside in the confidence intervals.
Highlights
Studying the relationship between two random variables is a very important issue in statistics
Consider a survival time study, where a sequence of possibly censored failure times is observed with d-dimensional covariate The main goal of this article is to establish the asymptotic normality of the kernel estimator of the relative error regression function when the data exhibit some kind of dependency
In the statistical literature it is very common to assume that (T, X) and C are independent. Under this assumption a lot of work has been done on the nonparametric estimation of the regression operator issue from T = m(X) + ε where ε is the observation error term
Summary
Studying the relationship between two random variables is a very important issue in statistics. The advantage of using the mean squared relative error as loss function is that is robust to outliers (see : [16], [18] and [23]) Having in mind such kind of data, [20] extend the work of [13] to the case of a relative error regression (RER) model. They established the uniform strong consistency and the asymptotic normality of the RER function estimator. No simulation study has been done to comfort the theoretical result We follow their approach, except that we assume that the data are dependent which is a very common case in practice.
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