Convergence Rates for $U$-Statistics and Related Statistics

Weak Convergence of Generalized U - Statistics

Convergence of U-statistics for interacting particle systems

The convergence of U -statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, dlPG99]. When dealing with Feynman-Kac and other interacting particle systems of Monte Carlo type, one faces a new type of problem. Namely, in a sample of N particles obtained through the cor...

Asymptotics for the Moment Convergence of U-Statistics in LIL

A Remark on Convergence in Distribution of U-statistics

It is proved that, for h measurable and symmetric in its arguments and Xi i.i.d., if the sequence {n−m2 ∑ i1,...,im≤n ij 6=ik if j 6=k h(Xi1 ,...,Xim )}n=1, is stochastically bounded, then Eh2<∞ and Eh(X1,x2,...,xm)=0 a.s.

Statistics for dental researcher, Part 2: Descriptive statistics

Descriptive statistics is the process of summarizing gathered raw data from a research and creating useful statistics, which help the better understanding of data. According to the types of variables, which consist of qualitative and quantitative variables, some descriptive statistics have been introduced. Frequency percentage is used in qualitative data, and mean, median, mode, standard deviat...