Non standard functional limit laws for the increments of the compound empirical distribution function

Details Non standard functional limit laws for the increments of the compound empirical distribution function Non standard functional limit laws for the increments of the compound empirical distribution function

2012-01-26

arxiv.org/abs/1201.5528v1

Mathematics

Statistics Theory

Scientific paper

Let $(Y_i,Z_i)_{i\geq 1}$ be a sequence of independent, identically distributed (i.i.d.) random vectors taking values in $\RRR^k\times\RRR^d$, for some integers $k$ and $d$. Given $z\in \RRR^d$, we provide a nonstandard functional limit law for the sequence of functional increments of the compound empirical process, namely $$\mathbf{\Delta}_{n,\cc}(h_n,z,\cdot):= \frac{1}{nh_n}\sliin 1_{[0,\cdot)}\poo \frac{Z_i-z}{{h_n}^{1/d}}\pff Y_i.$$ Provided that $nh_n\sim c\log n $ as $\nif$, we obtain, under some natural conditions on the conditional exponential moments of $Y\mid Z=z$, that $$\mathbf{\Delta}_{n,\cc}(h_n,z,\cdot)\leadsto \Gam\text{almost surely},$$ where $\leadsto$ denotes the clustering process under the sup norm on $\Idd$. Here, $\Gam$ is a compact set that is related to the large deviations of certain compound Poisson processes.

Affiliated with

Also associated with

No associations

Rating

Non standard functional limit laws for the increments of the compound empirical distribution function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non standard functional limit laws for the increments of the compound empirical distribution function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non standard functional limit laws for the increments of the compound empirical distribution function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-445716