Estimation of the variance-time and covariance-time curves of a stationary point process

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Abstract
Cox and Lewis (1966) propose estimators of the variance-time and covariance-time curves of a stationary point process. Continuous analogues of these estimators are considered in this paper. Asymptotic distributions of these statistics are obtained under the null hypotheses that the observations are generated by circular uniform and Poisson processes. In the first case, the statistics considered are generalizations of a statistic considered by Ajne (1968) and Watson (1967) as a test of circular uniformity. In the latter, these estimators are shown to be asymptotically normal. Numerical comparisons and computing formulas are given in the final section.

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