Nonparametric estimation of the hazard function based on delta-records

R. Gouet Bañares, F. J. López Lorente, L. P. Maldonado Guaje, G. Sanz Sáiz

Some nonparametric procedures for the estimation of the hazard function based on record values have been considered in the literature. These methods use multiple samples of records since a unique sample does not provide good results. In this work we show how delta-records can be used to yield nonparametric estimators of the hazard function, both in continuous and discrete distributions, using only one sample. In the discrete case, the likelihood of the delta-record sample is written in terms of the hazard function, thus allowing its estimation. The continuous case is carried out by discretizing the distribution, applying the discrete estimator and smoothing the result. We analyze the results via simulation and show that delta-records provide good estimations, specially for light and medium-tailed distributions.

Palabras clave: delta-records nonparametric estimation hazard function.

M. I. Borrajo García, W. González Manteiga, M. D. Martínez Miranda

M. Conde Amboage, V. Patilea, C. Sánchez Sellero