Discrete triangular distributions and non-parametric estimation for probability mass function

Célestin Kokonendji (1) , Tristan Senga Kiessé (1) , Silvio S. Zocchi (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 ESALQ - Escola Superior de Agricultura "Luiz de Queiroz"

Discrete triangular distributions are introduced, in order to serve as kernels in the non-parametric estimation for probability mass function. They are locally symmetric around every point of estimation. Their variances depend on the smoothing bandwidth and establish a bridge between Dirac and discrete uniform distributions. The boundary bias related to the discrete triangular kernel estimator is solved through a modification of the kernel near the boundary. The mean integrated squared errors and then the optimal bandwidth are investigated. We also study the adequate bandwidth for excess zeros. The performance of the discrete triangular kernel estimator is illustrated using simulated count data. An application to count data from football is described and compared with a binomial kernel estimator.

Mots clés: Boundary bias; Count data; Discrete kernel estimator; Excess zeros; Variable kernel estimate

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

Célestin Kokonendji, Tristan Senga Kiessé, Silvio S. Zocchi. Discrete triangular distributions and non-parametric estimation for probability mass function. Journal of Nonparametric Statistics, 2007, 19 (6-8), pp.241-254. ⟨10.1080/10485250701733747⟩. ⟨hal-00947709⟩