Jacob, Pierre Estimation du contour discontinu d’un processus ponctuel sur le plan. (Estimation of the discontinuous contour of a point process in the plane). (French) Zbl 0652.62086 Publ. Inst. Stat. Univ. Paris 29, No. 3-4, 1-26 (1984). Summary: The spectrum of a point process is supposed to be defined on the plane by: \(\{\) (x,y)\(\in {\mathbb{R}}^ 2:\) \(0\leq x\leq 1\); \(0<y<\max (\phi (x);\phi (x\)-))\(\}\) where \(\phi\) is a right continuous with left-hand limits function. We study sufficient conditions of stochastic convergence to \(\phi\) in the L p-norm or in the Skorokhod topology of some estimates. The limit law is found in a particular case. We also give estimates of jumps and of their sizes. Cited in 4 Documents MSC: 62M09 Non-Markovian processes: estimation 62E20 Asymptotic distribution theory in statistics 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 62G05 Nonparametric estimation 60F25 \(L^p\)-limit theorems Keywords:efficiency; asymptotic normality; almost sure convergence; spectrum of a point process; Skorokhod topology; estimates of jumps PDFBibTeX XMLCite \textit{P. Jacob}, Publ. Inst. Stat. Univ. Paris 29, No. 3--4, 1--26 (1984; Zbl 0652.62086)