Limit laws for maxima of a stationary random sequence with random sample size

• Autores: A. Freitas, Jürg Hüsler, M. Graça Temido
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 21, Nº. 1, 2012, págs. 116-131
• Idioma: inglés
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• Resumen

  • Let {X n } be a stationary sequence and {k n } be a nondecreasing sequence such that k n+1/k n →r≥1. Assume that the limit distribution G of Mkn with an appropriate linear normalization exists. We consider the maxima M n =max {X i ,i≤n} sampled at random times T n , where T n /k n converges in probability to a positive random variable D, and show that the limit distribution of MTn exists under weak mixing conditions. The limit distribution of MTn is a mixture of G and the distribution of D.