113
Views
0
CrossRef citations to date
0
Altmetric
Articles

Estimating intensity functions of spatial inhomogeneous Poisson point processes via a Stein estimator

& ORCID Icon
Pages 4816-4848 | Received 09 Jan 2021, Accepted 15 Aug 2021, Published online: 09 Sep 2021

References

  • Adams, R. A., and J. F. Fournier. 2003. Sobolev Spaces. Vol. 140. Cambridge: Academic Press.
  • Andrews, J. G., S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang. 2014. What will 5G be? IEEE Journal on Selected Areas in Communications 32 (6):1065–82. doi:10.1109/JSAC.2014.2328098.
  • Bresler, G., and D. Nagaraj. 2019. Stein’s method for stationary distibutions of Markov chains and application to Ising models. Annals of Applied Probability 29 (5):3230–65.
  • Cabella, P., and D. Marinucci. 2009. Statistical challenges in the analysis of cosmic microwave background radiation. The Annals of Applied Statistics 3 (1):61–95. doi:10.1214/08-AOAS190.
  • Clausel, M., J. F. Coeurjolly, and J. Lelong. 2016. Stein estimation of the intensity of a spatial homogeneous poisson point process. Annals of Applied Probability 26 (3):1495–534.
  • Dai, J. G., and W. Dai. 1999. A heavy traffic limit theorem for a class of open queueing networks with finite buffers. Queueing Systems 32 (1/3):5–40. doi:10.1023/A:1019178802391.
  • Dai, W. 1997. Brownian approximations for queueing networks with finite buffers: Modeling, heavy traffic analysis and numerical implementations. PhD thesis, The Georgia Institute of Technology, 1996, Published in UMI Dissertation Services, A Bell & Howell Company, Michigan, USA.
  • Dai, W. 2013. Optimal rate scheduling via utility-maximization for J-user MIMO Markov fading wireless channels with cooperation. Operations Research 61 (6):1450–62. doi:10.1287/opre.2013.1224.
  • Dai, W. 2018a. A unified system of FB-SDEs with Levy jumps and double completely-S skew reflections. Communications in Mathematical Sciences 16 (3):659–704. doi:10.4310/CMS.2018.v16.n3.a4.
  • Dai, W. 2018b. Platform modelling and scheduling game with multiple intelligent cloud-computing pools for big data. Mathematical and Computer Modelling of Dynamical Systems 24 (5):526–52. doi:10.1080/13873954.2018.1516677.
  • Dai, W. 2019a. AI based simulation and analysis by Malliavin calculus for backward stochastic partial differential equations. Proceeding (Preprints) of 21th Annual Conference of Jiangsu Association of Applied Statistics, Pages 27–69. June 14-16,
  • Dai, W. 2019b. Quantum-computing with AI & blockchain: Modelling, fault tolerance and capacity scheduling. Mathematical and Computer Modelling of Dynamical Systems 25 (6):523–59. doi:10.1080/13873954.2019.1677725.
  • Daley, D. J., and D. Vere-Jones. 2003. An introduction to the theory of point processes. Vol. I. Probability and its applications. New York: Springer-Verlag.
  • Daley, D. J., and D. Vere-Jones. 2008. An introduction to the theory of point Processes. Vol. II. Probability and its applications. 2nd ed. New York: Springer.
  • De Mauro, A., M. Greco, and M. Grimaldi. 2016. A formal definition of big data based on its essential features. Library Review 65 (3):122–35. doi:10.1108/LR-06-2015-0061.
  • Dedić, N., and C. Stanier. 2017. Towards differentiating business intelligence, big data, data analytics and knowledge discovery. Vol. 285. Berlin, Heidelberg: Springer International Publishing.
  • Ethier, S. N., and T. G. Kurtz. 1986. Markov processes: Characterization and convergence. New York: John Wiley & Sons Inc.
  • Kuznetsov, N. Y. 2018. A heuristic algorithm to control conflicting nonstationary traffic flows. Cybernetics and Systems Analysis 54 (5):707–9. doi:10.1007/s10559-018-0072-6.
  • Lyrio, M. S., G. M. S. de Sa, H. D. Ventura, W. L. D. Assis, E. Villa, and P. R. Rios. 2020. Transformations with inhomogeneous nucleation and growth velocity. Journal of Materials Research and Technology 9 (5):9868–81. doi:10.1016/j.jmrt.2020.06.064.
  • Møller, J., and R. P. Waagepetersen. 2004. Statistical inference and simulation for spatial point processes. Boca Raton, FL: Chapman and Hall/CRC.
  • Niknam, S., H. Mehrpouyan, and B. Natarajan. 2017. A spatial spectral interference model for millimeter wave 5G applications. 2017 IEEE 86th Vehicular Technology Conference (VTC-Fall), 1–5. doi:10.1109/VTCFall.2017.8288066.
  • Nunno, G. D., B. Sendal, and F. Proske. 2009. Malliavin calculus for Lévy processes with applications to finance. Berlin: Springer-Verlag.
  • Pasupathy, R. 2011. Generating nonhomogeneous Poisson processes. Hoboken, NJ: John Wiley & Sons, Inc.
  • Privault, N., and A. Réveillac. 2008. Stein estimation for the drift of Gaussian processes using the Malliavin calculus. The Annals of Statistics 36 (5), 2531C2550. doi:10.1214/07-AOS540.
  • Privault, N., and A. Réveillac. 2009. Stein estimation of Poisson process intensities. Statistical Inference for Stochastic Processes 12 (1):37–53. doi:10.1007/s11203-007-9018-8.
  • Resnick, S. 1992. Adventures in stochastic processes. Boston: Birhäuser.
  • Rios, P. R., D. Jardim, W. L. D. Assis, T. C. Salazar, and E. Villa. 2009. Inhomogeneous Poisson point process nucleation: Comparison of analytical solution with cellular automata simulation. Materials Research 12 (2):219–24. doi:10.1590/S1516-14392009000200017.
  • Rubinstein, R. Y., and A. Shapiro. 1993. Discrete event systems, Wiley series in probability and mathematical statistics: Probability and mathematical statistics. Hoboken, NJ: John Wiley & Sons.
  • Shen, X., H. Chen, J. Dai, and W. Dai. 2002. The finite element method for computing the stationary distribution of an SRBM in a hypercube with applications to finite buffer queueing networks. Queueing Systems 42 (1):33–62. doi:10.1023/A:1019942711261.
  • Stein, C. 1981. Estimation of the mean of a multivariate normal distribution. Annals of Statistics 9 (6):1135–51.
  • Stein, M. L. 2007. Spatial variation of total column ozone on a global scale. The Annals of Applied Statistics 1 (1):191–210. doi:10.1214/07-AOAS106.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.