Approximations of empirical probability generating processes

Szűcs Gábor

Statistics & Risk Modeling, 2005, vol. 23, issue 1, 67-80

Abstract: First we polish an argument of Rémillard and Theodorescu for the weak convergence of the empirical probability generating process. Then we prove a general inequality between probability generating processes and the corresponding empirical processes, which readily implies a rate of convergence and trivializes the problem of weak convergence: whenever the empirical process or its non-parametric bootstrap version, or the parametric estimated empirical process or its bootstrap version converges, so does the corresponding probability generating process. Derivatives of the generating process are also considered.

Date: 2005
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DOI: 10.1524/stnd.2005.23.1.67

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