Asymptotic Properties of Random Weighted Empirical Distribution Function |
| |
| Authors: | Gaoge Hu Shesheng Gao Yongmin Zhong Chengfan Gu |
| |
| Institution: | 1. School of Automatics, Northwestern Polytechnical University, Xi'an, Shaanxi, Chinahugaoge1111@126.com;3. School of Automatics, Northwestern Polytechnical University, Xi'an, Shaanxi, China;4. School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Bundoora, Australia |
| |
| Abstract: | This article studies the asymptotic properties of the random weighted empirical distribution function of independent random variables. Suppose X1, X2, ???, Xn is a sequence of independent random variables, and this sequence is not required to be identically distributed. Denote the empirical distribution function of the sequence by Fn(x). Based on the random weighting method and Fn(x), the random weighted empirical distribution function Hn(x) is constructed and the asymptotic properties of Hn are discussed. Under weak conditions, the Glivenko–Cantelli theorem and the central limit theorem for the random weighted empirical distribution function are obtained. The obtained results have also been applied to study the distribution functions of random errors of multiple sensors. |
| |
| Keywords: | Central limit theorem Empirical distribution function Glivenko–Cantelli theorem Random weighting method |
|
|
