Detection of suspicious areas in non-stationary Gaussian fields and locally averaged non-Gaussian linear fields

被引：1
作者：
Steland, Ansgar [1 ]
机构：
[1] Rhein Westfal TH Aachen, Inst Stat, Wullnerstr 3, D-52056 Aachen, Germany
来源：
JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2025年 / 238卷
关键词：
Extremes; Image data; MR imaging; Spatial linear process; Refinement RS Integration; Strong approximation; FALSE DISCOVERY RATE; LIMIT-THEOREMS; PARTIAL SUMS; EXTREMES; APPROXIMATION; ASYMPTOTICS; MAXIMA; MODEL; LAWS;
D O I：
10.1016/j.jspi.2025.106273
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Gumbel-type extreme value theory for arrays of discrete Gaussian random fields is studied and applied to some classes of discretely sampled approximately locally self-similar Gaussian processes, especially micro-noise models. Non-Gaussian discrete random fields are handled by considering the maximum of local averages of raw data or residuals. Based on some novel weak approximations with rate for (weighted) partial sums for spatial linear processes including results under a class of local alternatives, sufficient conditions for Gumbel-type asymptotics of maximum-type detection rules to detect peaks and suspicious areas in image data and, more generally, random field data, are established. The results are examined by simulations and illustrated by analyzing CT brain image data.
引用
收藏
页数：25
相关论文
共 54 条
  • [1] Adler R.J., The Geometry of Random Fields, (1981)
  • [2] Arganda-Carreras I., Sorzano C., Carazo J.-M., Solorzano C., Kybic J., Consistent and elastic registration of histological sections using vector-spline regularization, Lect. Notes Comput. Sci. CVAMIA: Comput. Vis. Approach. Med. Image Anal., 4241, pp. 85-95, (2006)
  • [3] Benjamini Y., Hochberg Y., Controlling the false discovery rate: a practical and powerful approach to multiple testing, J. R. Stat. Soc. Ser. B Stat. Methodol., 57, 1, pp. 289-300, (1995)
  • [4] Berkes I., Liu W., Wu W.B., Komlós-Major-Tusnády approximation under dependence, Ann. Probab., 42, 2, pp. 794-817, (2014)
  • [5] Berkes I., Morrow G.J., Strong invariance principles for mixing random fields, Z. Wahrscheinlichkeitstheor. Verwandte Geb., 57, 1, pp. 15-37, (1981)
  • [6] Berman S.M., Limit theorems for the maximum term in stationary sequences, Ann. Math. Stat., 35, pp. 502-516, (1964)
  • [7] Berman S.M., Sojourns and extremes of Gaussian processes, Ann. Probab., 2, pp. 999-1026, (1974)
  • [8] Bickel P., Rosenblatt M., Two-dimensional random fields, Multivariate Analysis, III (Proc. Third Internat. Sympos., Wright State Univ., Dayton, Ohio, 1972), pp. 3-15, (1973)
  • [9] Bickel P.J., Wichura M.J., Convergence criteria for multiparameter stochastic processes and some applications, Ann. Math. Stat., 42, pp. 1656-1670, (1971)
  • [10] Bulinski A., Shashkin A., Strong invariance principle for dependent random fields, Dynamics & Stochastics, IMS Lecture Notes Monogr. Ser., 48, pp. 128-143, (2006)
123456