Topic
Scheffé’s lemma
About: Scheffé’s lemma is a research topic. Over the lifetime, 1 publications have been published within this topic receiving 5 citations.
Papers
TL;DR: In this article, a generalized version of a multiple Wiener integral is proposed to estimate conditional U-statistics with respect to the conditional distribution of a sequence of i.i.d. bi-variate vectors.
Abstract: Let{(Xn, Yn)}n⩾1 be a sequence of i.i.d. bi-variate vectors. In this article, we study the possible limit distributions ofU
n
h
(t), the so-calledconditional U-statistics, introduced by Stute.(10) They are estimators of functions of the formm
h
(t)=E{h(Y
1,...,Y
k
)|X
1=t
1,...,X
k
=t
k
},t=(t
1,...,t
k
)∈ℝ
k
whereE |h|<∞. Heret is fixed. In caset
1=...=tk=t (say), we describe the limiting random variables asmultiple Wiener integrals with respect toP
t, the conditional distribution ofY, givenX=t. Whent
i, 1⩽i⩽k, are not all equal, we introduce and use a slightly generalized version of a multiple Wiener integral.
18 citations
Performance Metrics
| Year | Papers |
|---|---|
| 1995 | 1 |