Seminar by Dr. Junho Yang（Hybrid）
- 【Date&Time】
- 13 March,2025 (Thursday) 15:30-16:30
Admission Free, No Booking Necessary
- 【Place】
- The Institute of Statistical Mathematics 3F Seminar Room5
+ Zoom (https://us06web.zoom.us/j/81357665887?pwd=lutSmXRdCvHbKfKfjXD37DoULefhNG.1)
- 【Speaker】
- Dr. Junho Yang
- 【Title】
- Pseudo-spectra of multivariate inhomogeneous spatial point processes
- 【Abstract】
- In this presentation, we propose a spectral method for multivariate inhomogeneous spatial point processes. A key ingredient is utilizing the asymptotic behavior of the periodogram. The periodogram is an asymptotically unbiased estimator of the spectrum of a second-order stationary point process. By extending this property, we show that under inhomogeneity, the expectation of the periodogram also converges to a matrix-valued function, which we refer to as the pseudo-spectrum. The pseudo-spectrum shares similar properties with the spectrum of stationary processes and can be interpreted using local parameters. We derive a consistent estimator of the pseudo-periodogram through kernel smoothing and propose two bandwidth selection methods. The performance and utility of our frequency domain methods are illustrated through simulation studies and a real data analysis of rainforest data.
This work is jointly done with Qi-Wen Ding (Academia Sinica) and Joonho Shin (Sungshin Women's University).
