Degenerate U− and V−statistics have asymptotic distributions that are given by an infinite weighted sum of χ2 random variables, whose weights are the eigenvalues of an integral operator whose solution is in general very difficult. We provide a new computational approximation of the eigenvalues and of the asymptotic distribution. As an illustration, we show that our algorithm is able to recover the tabulated asymptotic distribution of the Cramér-von Mises statistic.

Approximating weighted chi-square distributions

SERI, RAFFAELLO
2006-01-01

Abstract

Degenerate U− and V−statistics have asymptotic distributions that are given by an infinite weighted sum of χ2 random variables, whose weights are the eigenvalues of an integral operator whose solution is in general very difficult. We provide a new computational approximation of the eigenvalues and of the asymptotic distribution. As an illustration, we show that our algorithm is able to recover the tabulated asymptotic distribution of the Cramér-von Mises statistic.
2006
Atti del Convegno SER2006, Convegno Nazionale delle Ricerche sulle Serie Temporali
Convegno SER2006, Convegno Nazionale delle Ricerche sulle Serie Temporali
Monte Porzio Catone
18-19 April 2006
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1503510
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