Discussiones Mathematicae Probability and Statistics 25(1) (2005) 5-37

ESTIMATION OF THE HAZARD RATE FUNCTION WITH A REDUCTION OF BIAS AND VARIANCE AT THE BOUNDARY

Bożena Janiszewska and Roman Różański

Institute of Mathematics and Informatics
Wrocław University of Technology
Wybrzeże Wyspiańskiego 27, PL 50-370 Wrocław, Poland

e-mail: Bozena.Janiszewska@pwr.wroc.pl
e-mail: Roman.Rozanski@pwr.wroc.pl

Abstract

In the article, we propose a new estimator of the hazard rate function in the framework of the multiplicative point process intensity model. The technique combines the reflection method and the method of transformation. The new method eliminates the boundary effect for suitably selected transformations reducing the bias at the boundary and keeping the asymptotics of the variance. The transformation depends on a pre-estimate of the logarithmic derivative of the hazard function at the boundary.

Keywords: hazard rate function, multiplicative intensity point process model, Ramlau-Hansen kernel estimator, reduction of the bias, reflection, transformation.

2000 Mathematics Subject Classification: 62G05 , 62N02 , 62M99.

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Received 20 July 2003