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A cross-validation-...
A cross-validation-based statistical theory for point processes
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- Cronie, Ottmar, 1979 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology
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- Moradi, Mehdi (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University
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- Biscio, Christophe A. N. (författare)
- Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark,Aalborg Universitet,Aalborg University
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(creator_code:org_t)
- Oxford University Press, 2024
- 2024
- Engelska.
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Ingår i: Biometrika. - : Oxford University Press. - 0006-3444 .- 1464-3510. ; 111:2, s. 625-641
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Abstract
Ämnesord
Stäng
- Motivated by the general ability of cross-validation to reduce overfitting and mean square error, we develop a cross-validation-based statistical theory for general point processes. It is based on the combination of two novel concepts for general point processes: cross-validation and prediction errors. Our cross-validation approach uses thinning to split a point process/pattern into pairs of training and validation sets, while our prediction errors measure discrepancy between two point processes. The new statistical approach, which may be used to model different distributional characteristics, exploits the prediction errors to measure how well a given model predicts validation sets using associated training sets. Having indicated that our new framework generalizes many existing statistical approaches, we then establish different theoretical properties for it, including large sample properties. We further recognize that nonparametric intensity estimation is an instance of Papangelou conditional intensity estimation, which we exploit to apply our new statistical theory to kernel intensity estimation. Using independent thinning-based cross-validation, we numerically show that the new approach substantially outperforms the state-of-the-art in bandwidth selection. Finally, we carry out intensity estimation for a dataset in forestry and a dataset in neurology.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- Kernel intensity estimation
- Papangelou conditional intensity
- Prediction
- Spatial statistics
- Thinning
- Kernel intensity estimation; Papangelou conditional intensity; Prediction; Spatial statistics; Thinning
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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