Consistent estimation of the intensity function of a cyclic Poisson process

Predicting a cyclic Poisson process

“…which is the kernel-type estimator of the intensity function¸of X introduced in Helmers et al (2003) and investigated also in Helmers et al (2005). Here, h n is a sequence of positive real numbers such that h n # 0, as n !…”

“…This assumption is a rather mild one since the set of all Lebesgue point of¸is dense in R, whenever¸is assumed to be locally integrable. The Lebesgue point assumption also occurs in Helmers et al (2003) and Helmers et al (2005).…”

Consistency of a Kernel-Type Estimator of the Intensity of the Cyclic Poisson Process With the Linear Trend

“…(9) Now note that the estimatorλ c,n (s) given in (9) is a special case of the estimator λ c,n,K (s) in (3), that is in (9) we use the uniform kernelK = In Helmers and Mangku [2] has been proved the following lemma.…”

“…a = 0, (cf. [3], [4], [6], section 2.3 of [7]) to the more general model (1). Suppose now that, for some ω ∈ Ω, a single realization N (ω) of the Poisson process N defined on a probability space (Ω, F, P) with intensity function λ (cf.…”

“…A review of such applications can be seen in [3], and a number of them can also be found in [1], [5], [7], [9] and [10].…”