TY - JOUR

T1 - Limit laws for the number of near-maxima via the Poisson approximation

AU - Pakes, Anthony

AU - Li, Y.

PY - 1998

Y1 - 1998

N2 - Given a sequence of i.i.d. random variables, new proofs are given for limit theorems for the number of observations near the maximum up to time n, as n --> infinity. The proofs rely on a Poisson approximation to conditioned binomial laws, and they reveal the origin in the limit laws of mixing with respect to extreme value laws. For the case of attraction to the Frechet law, the effects of relaxing a technical condition are examined. The results are set in the broader context of counting observations near upper order statistics. This involves little extra effort. (C) 1998 Elsevier Science B.V. All rights reserved.

AB - Given a sequence of i.i.d. random variables, new proofs are given for limit theorems for the number of observations near the maximum up to time n, as n --> infinity. The proofs rely on a Poisson approximation to conditioned binomial laws, and they reveal the origin in the limit laws of mixing with respect to extreme value laws. For the case of attraction to the Frechet law, the effects of relaxing a technical condition are examined. The results are set in the broader context of counting observations near upper order statistics. This involves little extra effort. (C) 1998 Elsevier Science B.V. All rights reserved.

U2 - 10.1016/S0167-7152(98)00148-5

DO - 10.1016/S0167-7152(98)00148-5

M3 - Article

VL - 40

SP - 395

EP - 401

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

ER -