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On the weak convergence of a class of estimators of the variance-time curve of a weakly stationary point process

Published online by Cambridge University Press:  14 July 2016

A. M. Liebetrau
A. M. Liebetrau*
Affiliation:
The Johns Hopkins University
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Abstract

The second-moment structure of an estimator V*(t) of the variance-time curve V(t) of a weakly stationary point process is obtained in the case where the process is Poisson. This result is used to establish the weak convergence of a class of estimators of the form Tβ(V*(tTα) – V(tTα)), 0 < α < 1, to a non-stationary Gaussian process. Similar results are shown to hold when α = 0 and in the case where V(tTα) is replaced by a suitable estimator.

Keywords

WEAK CONVERGENCEVARIANCE-TIME CURVEPOINT PROCESSPOISSON PROCESSESTIMATOR
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 1 , March 1977 , pp. 114 - 126
Copyright
Copyright © Applied Probability Trust 1977 

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