On δ-record observations: asymptotic rates for the counting process and elements of maximum likelihood estimation

• Autores: Raúl Gouet Bañares, Gerardo Sanz Sáiz, Francisco Javier López Lorente
• 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. 188-214
• Idioma: inglés
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• Resumen

  • Given a sequence of random variables {X n ,n≥1} and δ∈ℝ, an observation X n is a δ-record if X n >max {X 1,…,X n−1}+δ. We obtain, for δ≤0, weak and strong laws of large numbers for the counting process of δ-records among the first n observations from a sequence of independent identically distributed random variables, with common distribution F, possibly discontinuous. We provide examples of our results in the context of common probability distributions. Finally, we show how δ-records can be used for maximum likelihood estimation.