2024년도 제 2회 BK 통계 세미나 개최를 안내드립니다.
고려대학교 통계학과 통계연구소, BK21 통계학교육연구팀과 DS+ 사업단 주최로 이루어지는 세미나입니다.
일시 : 2024년 02월 21일 (수) 오전 11시
장소 : 온라인(ZOOM)
연사 : 양준호 박사 (Institute of Statistical Science, Academia Sinica)
주제 :
Fourier Analysis of Spatial Point Processes
Abstract :
In this presentation, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point pattern and its tapered counterpart. Under second-order stationarity, we show that both the DFTs and the tapered DFTs are asymptotically jointly independent Gaussian even when the DFTs share the same limiting frequencies. Based on these results, we establish an alpha-mixing central limit theorem for a statistic formulated as a quadratic form of the tapered DFT. As applications, we derive the asymptotic distribution of the kernel spectral density estimator and establish a frequency domain inferential method for parametric stationary point processes. For the latter, the resulting model parameter estimator is computationally tractable and yields meaningful interpretations even in the case of model misspecification. We investigate the finite sample performance of our estimator through simulations, considering scenarios of both correctly specified and misspecified models. Furthermore, we extend our proposed DFT-based frequency domain methods to a class of non-stationary spatial point processes. Based on the joint work with Yongtao Guan (CUHK-Shenzhen).
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참가 Zoom 회의
https://korea-ac-kr.zoom.us/j/4145766503?pwd=FMeFToJRalvz6UDl8xOB9g1uQOyufg.1&omn=89053988454
회의 ID: 414 576 6503
암호: Kustat123@
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