Some uniform in bandwidth functional results for the tail uniform empirical and quantile processes

Details Some uniform in bandwidth functional results for the tail uniform empirical and quantile processes Some uniform in bandwidth functional results for the tail uniform empirical and quantile processes

2012-01-26

arxiv.org/abs/1201.5517v1

Mathematics

Statistics Theory

Scientific paper

For fixed $t\in [0,1)$ and $h>0$, consider the local uniform empirical
process $$\DD_{n,h,t}(s):=n^{-1/2}\coo\sliin 1_{[t,t+hs]}(U_i)-hs\cff,\;s\in
[0,1],$$ where the $U_i$ are independent and uniformly distributed on $[0,1]$.
We investigate the functional limit behaviour of $\DD_{n,h,t}$ uniformly in
$\wth_n\le h\le h_n$ when $n\wth_n/\log\log n\rar \infty$ and $h_n\rar 0$.

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