Asymptotic Properties of Random Weighted Empirical Distribution Function

作者：Hu, Gaoge^*; Gao, Shesheng; Zhong, Yongmin; Gu, Chengfan

来源：Communications in Statistics - Theory and Methods, 2015, 44(18): 3812-3824.

DOI：10.1080/03610926.2013.768669

• Central limit theorem
• Empirical distribution function
• Glivenko-Cantelli theorem
• Random weighting method

This article studies the asymptotic properties of the random weighted empirical distribution function of independent random variables. Suppose X-1, X-2, ..., X-n 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 F-n (x). Based on the random weighting method and F-n (x), the random weighted empirical distribution function H-n (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.

• 出版日期2015
• 单位西北工业大学