Functional Estimation of the Random Rate of a Cox Process
The intensity of a doubly stochastic Poisson process (DSPP) is also a stochastic process whose integral is the mean process of the DSPP. From a set of sample paths of the Cox process we propose a numerical method, preserving the monotone character of the mean, to estimate the intensity on the basis of the functional PCA. A validation of the estimation method is presented by means of a simulation as well as a comparison with an alternative estimation method.
KeywordsCox process Monotone piecewise cubic interpolation Functional principal component analysis Functional data analysis
AMS 2000 Subject Classification60G51 60G55 62H25 46N30
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