Semiparametric estimation for count data through weighted distributions

Célestin C. Kokonendji (1) , Tristan Senga Kiessé (1) , Narayanaswamy Balakrishnan (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 McMaster University [Hamilton, Ontario]

This paper is concerned with semiparametric discrete kernel estimators when the unknown count distribution can be considered to have a general weighted Poisson form. The estimator is constructed by multiplying the Poisson estimate with a nonparametric discrete kernel-type estimate of the Poisson weight function. Comparisons are then carried out with the ordinary discrete kernel probability mass function estimators. The Poisson weight function is thus a local multiplicative correction factor, and is considered as the uniform measure to detect departures from the equidispersed Poisson distribution. In this way, the effects of dispersion and zeroproportion with respect to the standard Poisson distribution are also minimized. This method of estimation is also applied to the weighted binomial form for the count distribution having a finite support. The proposed estimators, in addition to being simple, easy-to-implement and effective, also outperform the competing nonparametric and parametric estimators in finitesample situations. Two examples illustrate this new semiparametric estimation.

Mots clés: Bandwidth selection; Discrete kernel method; Discrete weighted distribution; Dispersion; Multiplicative correction factor; Zero-proportion

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Célestin C. Kokonendji, Tristan Senga Kiessé, Narayanaswamy Balakrishnan. Semiparametric estimation for count data through weighted distributions. Journal of Statistical Planning and Inference, 2009, 139 (10), pp.3625-3638. ⟨10.1016/j.jspi.2009.04.013⟩. ⟨hal-00947788⟩