Nonparametric inference for a doubly stochastic Poisson process

Klaus J. Utikal

Stochastic Processes and their Applications, 1993, vol. 45, issue 2, 331-349

Abstract: Consider a doubly stochastic Poisson process whose intensity [lambda]t is given by [lambda]t=[alpha](Zt), where [alpha] is an unknown nonrandom function of another (covariate) process Zt. Only one continuous time observation of counting and covariate process is available. The function is estimated and the normalized estimator is shown to converge weakly to a Gaussian process as time approaches infinity. Confidence bands for are given. A uniformly consistent estimator of [alpha] is obtained. Consistent tests for independence from the covariate process are proposed.

Date: 1993
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