Estimation of a distribution function using Lagrange polynomials with Tchebychev–Gauss points
Résumé
The estimation of the distribution function of a real random variable is an intrinsic topic in non parametric estimation. To this end, a distribution estimator based on Lagrange polynomials and Tchebychev-Gauss points, is introduced. Some asymptotic properties of the proposed estimator are investigated, such as its asymptotic bias, variance, mean squared error and Chung-Smirnov propriety. The asymptotic normality and the uniform convergence of the estimator are also established. Lastly, the performance of the proposed estimator is explored through a certain simulation examples.
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