No. 1081

Title:

A sufficient condition for observation noise not to affect the extreme value distribution

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics);
Shimura, Takaaki (The Institute of Statistical Mathematics)

Key words:

Extreme value distribution, sample maxima, observation noise, Orlicz norm.

Abstract:

    We present a sufficient condition under which the rescaled sample maxima of the data $ \{ X_{i} \} $ has the same asymptotic distribution as that of the data $ \{ X_{i} + e_{i} \} $ with observation noise $ e_i $. The condition is described in terms of the Orlicz norm.