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A limited in bandwidth uniformity for the functional limit law of the increments of the empirical process
Empricial processes Functional limit theorems Strong theorems Density estimation LATEX2ε
2009/9/16
Consider the following local empirical process indexed by $K in mathcal{G}$, for fixed $h>0$ and $z in mathbb{R}^d$: $$G_n(K,h,z):=sum_{i=1}^n K (frac{Z_i-z}{h^{1/d}}) - mathbb{E} (K (frac{Z_i-z}{h^{1...
A Limit Law for the Root Value of Minimax Trees
Minimax Tree Limit Law Weak Convergence Analysis of Algorithms Gametree
2009/4/27
We consider minimax trees with independent, identically distributed leaf values that have a continuous distribution function FV being strictly increasing on the range where 0< FV <1. It was shown by P...
A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree
weak limit law random recursive tree random walk
2009/3/23
We present a short probabilistic proof of a weak convergence result for the number of cuts needed to isolate the root of a random recursive tree. The proof is based on a coupling related to a certain ...