Argmax-stable marked empirical processes
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Contributors
Abstract
We consider a marked empirical process corresponding to a sample X1, ..., Xn of independent and identically distributed random variables and exchangeable random marks C1, ..., Cn. If the sum of all marks is equal to zero, then there exists a certain order statistic with random index, which is a maximizing point of the process. It is shown that for each finite sample size n ∈ N this point of maximum has the same distribution as X1 (argmax-stability). As an application we derive the exact distribution of an estimator for the discontinuity point in a regression function.
Details
Original language | English |
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Pages (from-to) | 1203-1206 |
Number of pages | 4 |
Journal | Statistics and Probability Letters |
Volume | 79 |
Issue number | 9 |
Publication status | Published - 1 May 2009 |
Peer-reviewed | Yes |