Delta-records with linear trend.

M. Lafuente Blasco, G. Sanz Sáiz, F. J. López Lorente, R. Gouet Bañares

An extension of the concept of record called delta-record is analyzed. Given a sequence of random variables X_i, an observation X_n is a delta-record if X_j > max(X_1,X_2,…, X_(n-1))+delta, with delta being a real number. The interest of delta-records comes from the fact that they are more frequent than records when delta<0, which increases the potential applications.
For the case where the observations are drawn from time-series of the form Y_n=X_n+ c . n, with X_n i.i.d. and c is a drift, we characterize the asymptotic behavior of the number of delta-records when considering different scenarios depending on the sign of the drift and the value of delta. This model, known as Linear Drift Model (LDM), has attracted much attention in recent years, specially in physics literature.
In the regime of small drift and small delta, we also extend known results, about the behavior of the probability of the n-th observation being a delta-record.
Finally, we apply our results to temperature data.

Palabras clave: Records, Delta-Records, Linear Trend, Asymptotics, Central Limit Theorem.

X05.2 Extremos y Estadísticos de Orden
7 de septiembre de 2016  12:30
0.09 - Aula de proyectos 2

M. Á. Sordo Díaz, A. Castaño Martínez, G. Pigueiras Voces

I. Montes, E. Miranda

A. J. Arriaza Gómez, M. Á. Sordo Díaz, A. Suárez Llorens