Prakasa Rao, B. L. S. ; Sen, Arusharka
(1995)
*Limit distributions of conditional U-statistics*
Journal of Theoretical Probability, 8
(2).
pp. 261-301.
ISSN 0894-9840

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Official URL: http://www.springerlink.com/content/7168215h112842...

Related URL: http://dx.doi.org/10.1007/BF02212880

## Abstract

Let{(X_{n}, Y_{n})}_{n ≥ 1} be a sequence of i.i.d. bi-variate vectors. In this article, we study the possible limit distributions of U^{h} _{n} (t), the so-called conditional U-statistics, introduced by Stute. ^{(10)} They are estimators of functions of the form m^{h}(t)=E{h(Y _{1},...,Y_{k})|X_{1}=t _{l},...,X_{k} = t_{k}},t=(t _{1},...,t_{k}) ∈R^{k} where E|h|<∞. Here t is fixed. In case t_{l}=...=t_{k}=t (say), we describe the limiting random variables as multiple Wiener integrals with respect to P_{t}, the conditional distribution of Y, given X=t. When t_{i}, 1≤i≤k, are not all equal, we introduce and use a slightly generalized version of a multiple Wiener integral.

Item Type: | Article |
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Source: | Coptright of this article belongs to Springer. |

Keywords: | Nonparametric Regression Estimation; Conditional U-statistics; Limit Distribution; Symmetric Tensor Product; Multiple Wiener Integral; Dynkin-Mandelbaum Decomposition; Scheffe's Lemma |

ID Code: | 37207 |

Deposited On: | 26 Apr 2011 10:48 |

Last Modified: | 26 Apr 2011 10:48 |

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