On Kernel Inverse Distribution Function Estimation Near the Boundary

ALMI, Nassima (2023) On Kernel Inverse Distribution Function Estimation Near the Boundary. Doctoral thesis, Université de mohamed kheider biskra.

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Abstract

This work is about a nonparametric approach of both cumulative distribution and quantile function to improve boundary effects in the kernel estimation method. It is very often the case that the natural support of a distribution to be estimated is not the whole real line but an interval bounded on one or both sides. Hence, the kernel distribution estimator may not provide appropriate estimates of the distribution function at such points. To remove this effect, a variety of methods have been developed in the literature, the most widely used is the reflection, the convex combination, ... In this thesis, we introduce a new method of boundary correction when estimating both cumulative distribution and quantile function. Our technique based on a self elimination between the Bias and the estimator it self. we turned out that, with an adequate choice of the parameters of the two proposed estimators, the rate of convergence of two estimators will be faster than the existing kernel proposed.

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