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Nonparametric estimation of renewal processes from count data
Author(s) -
Guédon Yann,
CocozzaThivent Christiane
Publication year - 2003
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316067
Subject(s) - count data , nonparametric statistics , event (particle physics) , mathematics , statistics , basis (linear algebra) , computer science , algorithm , mathematical optimization , geometry , poisson distribution , physics , quantum mechanics
The authors address the problem of estimating an inter‐event distribution on the basis of count data. They derive a nonparametric maximum likelihood estimate of the inter‐event distribution utilizing the EM algorithm both in the case of an ordinary renewal process and in the case of an equilibrium renewal process. In the latter case, the iterative estimation procedure follows the basic scheme proposed by Vardi for estimating an inter‐event distribution on the basis of time‐interval data; it combines the outputs of the E‐step corresponding to the inter‐event distribution and to the length‐biased distribution. The authors also investigate a penalized likelihood approach to provide the proposed estimation procedure with regularization capabilities. They evaluate the practical estimation procedure using simulated count data and apply it to real count data representing the elongation of coffee‐tree leafy axes.