ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Let μn be the empirical probability measure associated with n i.i.d. random vectors each having a uniform distribution in the unit square S of the plane. After μn is known, take the worst partition of the square into k≦n rectangles R i, each with its short side at least δ times as long as the long side, and let Z= n∑|μn(R j)−μ(R j)|. We prove distribution inequalities for Z implying the right half of c p,δ(n,k)p/2 ≦ EZ p ≦ C p,δ(n,k p/2, p 〉 0. (The left half follows easily by considering non-random partitions.) Similar results are obtained in other dimensions, and for population distributions other than uniform, and our results are related to data based histogram density estimation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00339939
Permalink