A CLT for weighted time-dependent uniform empirical processes

作者：Yang Yuping^*

来源：Journal of Statistical Planning and Inference, 2015, 157: 36-53.

DOI：10.1016/j.jspi.2014.09.002

• Weighted empirical processes
• Central limit theorem
• Convergence of stochastic processes

For a uniform process {X-t : t is an element of El (by which X-t is uniformly distributed on (0, 1) for t is an element of E) and a function w(x) > 0 on (0, 1), we give a sufficient condition for the weak convergence of the empirical process based on {w(x)(1(xt <= x) - x) t is an element of E, x is an element of [0, 1]) in l(infinity)(E x [0, 1]). When specializing to w(x) equivalent to 1 and assuming strict monotonicity on the marginal distribution functions of the input process, we recover a result of Kuelbs et al. (2013). In the last section, we give an example of the main theorem.

• 出版日期2015-3
• 单位西南大学