Discrete triangular associated kernel and bandwidth choices in semiparametric estimation for count data

Abstract

This work deals with semiparametric kernel estimator of probability mass functions which are assumed to be modified Poisson distributions. This semiparametric approach is based on discrete associated kernel method appropriated for modelling count data; in particular, the famous discrete symmetric triangular kernels are used. Two data-driven bandwidth selection procedures are investigated and an explicit expression of optimal bandwidth not available until now is provided. Moreover, some asymptotic properties of the cross-validation criterion adapted for discrete semiparametric kernel estimation are studied. Finally, to measure the performance of semiparametric estimator according to each type of bandwidth parameter, some applications are realized on three real count data-sets from sociology and biology.

Keywords:

• bootstrap methods
• cross-validation
• discrete associated kernel
• mean integrated squared error
• optimal bandwidth
• wood formation

AMS Subject Classification::

• Primary: 62G07
• 62F10
• Secondary: 62G20
• 62G99

Acknowledgements

The authors are grateful to an anonymous referee whose comments improved this paper.