Regression and time series model selection in small samples
Abstract
A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better model order choices than any other asymptotically efficient method. Applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The authors used an all-subsets model selection approach with AICc as selection criteria to account for limited sample size.
“We used an all‐subsets model selection approach (due to the small model set), with Akaike's Corrected Information Criterion (AICc) as our selection criteria to account for our limited sample size (Hurvich and Tsai 1989).”
From River Otter Predation of Nesting Seabirds Along the Coasts of North America (2025) · cites this paper as Hurvich and Tsai 1989
Cites
The Relationship Between Variable Selection and Data Agumentation and a Method for Prediction
Allen, D. M. (1974) · Technometrics · doi:10.1080/00401706.1974.10489157 · Cited by 1,469 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Multimodel Inference: Understanding AIC and BIC in Model Selection
Burnham, K. P., & Anderson, D. R. (2004) · Sociological Methods & Research · doi:10.1177/0049124104268644 · Cited by 11,648 · see citing works
Burnham, K. P., Anderson, D. R., & Huyvaert, K. P. (2011) · Behavioral Ecology and Sociobiology · doi:10.1007/s00265-010-1029-6 · Cited by 4,104 · see citing works
Posada, D., & Buckley, T. R. (2004) · Systematic Biology · doi:10.1080/10635150490522304 · Cited by 3,927 · see citing works
Phylogenomics resolves the timing and pattern of insect evolution
Misof, B., Liu, S., Meusemann, K., Peters, R. S., Donath, A., Mayer, C., Frandsen, P. B., Ware, J., Flouri, T., Beutel, R. G., et al. (2014) · Science · doi:10.1126/science.1257570 · Cited by 2,694 · see citing works
Model selection for ecologists: the worldviews of AIC and BIC
Aho, K., Derryberry, D., & Peterson, T. (2014) · Ecology · doi:10.1890/13-1452.1 · Cited by 1,165 · see citing works
Impact of biochar and hydrochar addition on water retention and water repellency of sandy soil
Abel, S., Peters, A., Trinks, S., Schonsky, H., Facklam, M., & Wessolek, G. (2013) · Geoderma · doi:10.1016/j.geoderma.2013.03.003 · Cited by 785 · see citing works
Kernel methods in system identification, machine learning and function estimation: A survey
Pillonetto, G., Dinuzzo, F., Chen, T., De Nicolao, G., & Ljung, L. (2014) · Automatica · doi:10.1016/j.automatica.2014.01.001 · Cited by 741 · see citing works
Makkonen, M., Berg, M. P., Handa, I. T., Hättenschwiler, S., van Ruijven, J., van Bodegom, P. M., & Aerts, R. (2012) · Ecology Letters · doi:10.1111/j.1461-0248.2012.01826.x · Cited by 502 · see citing works
Topological organization of the human brain functional connectome across the lifespan
Cao, M., Wang, J.-H., Dai, Z.-J., Cao, X.-Y., Jiang, L.-L., Fan, F.-M., Song, X.-W., Xia, M.-R., Shu, N., Dong, Q., et al. (2014) · Developmental Cognitive Neuroscience · doi:10.1016/j.dcn.2013.11.004 · Cited by 440 · see citing works
Marine plastic debris emits a keystone infochemical for olfactory foraging seabirds
Savoca, M. S., Wohlfeil, M. E., Ebeler, S. E., & Nevitt, G. A. (2016) · Science Advances · doi:10.1126/sciadv.1600395 · Cited by 322 · see citing works
Comparing dynamic causal models using AIC, BIC and free energy
Penny, W. D. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2011.07.039 · Cited by 298 · see citing works
Wolves–coyotes–foxes: a cascade among carnivores
Levi, T., & Wilmers, C. C. (2012) · Ecology · doi:10.1890/11-0165.1 · Cited by 293 · see citing works
Stable isotope-based diet reconstructions of Turkana Basin hominins
Cerling, T. E., Manthi, F. K., Mbua, E. N., Leakey, L. N., Leakey, M. G., Leakey, R. E., Brown, F. H., Grine, F. E., Hart, J. A., Kaleme, P., et al. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1222568110 · Cited by 235 · see citing works
Likelihood ratios: A simple and flexible statistic for empirical psychologists
Glover, S., & Dixon, P. (2004) · Psychonomic Bulletin & Review · doi:10.3758/bf03196706 · Cited by 218 · see citing works
Lassopack: model selection and prediction with regularized regression in Stata
Ahrens, A., Hansen, C. B., & Schaffer, M. E. (2020) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x20909697 · Cited by 212 · see citing works
Tolerant food sharing and reciprocity is precluded by despotism among bonobos but not chimpanzees
Jaeggi, A. V., Stevens, J. M. G., & Van Schaik, C. P. (2010) · American Journal of Physical Anthropology · doi:10.1002/ajpa.21288 · Cited by 205 · see citing works
Jelescu, I. O., Veraart, J., Adisetiyo, V., Milla, S. S., Novikov, D. S., & Fieremans, E. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2014.12.009 · Cited by 202 · see citing works
Selecting the Best Linear Mixed Model Under REML
Gurka, M. J. (2006) · The American Statistician · doi:10.1198/000313006x90396 · Cited by 200 · see citing works
Deep learning for small and big data in psychiatry
Koppe, G., Meyer-Lindenberg, A., & Durstewitz, D. (2021) · Neuropsychopharmacology · doi:10.1038/s41386-020-0767-z · Cited by 189 · see citing works
The effect of protein timing on muscle strength and hypertrophy: a meta-analysis
Schoenfeld, B. J., Aragon, A. A., & Krieger, J. W. (2013) · Journal of the International Society of Sports Nutrition · doi:10.1186/1550-2783-10-53 · Cited by 201 · see citing works
Schlichting, M. L., Guarino, K. F., Schapiro, A. C., Turk-Browne, N. B., & Preston, A. R. (2017) · Journal of Cognitive Neuroscience · doi:10.1162/jocn_a_01028 · Cited by 173 · see citing works
Virological factors that increase the transmissibility of emerging human viruses
Geoghegan, J. L., Senior, A. M., Di Giallonardo, F., & Holmes, E. C. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1521582113 · Cited by 155 · see citing works
Van Calster, B., van Smeden, M., De Cock, B., & Steyerberg, E. W. (2020) · Statistical Methods in Medical Research · doi:10.1177/0962280220921415 · Cited by 120 · see citing works
Decoding lifespan changes of the human brain using resting-state functional connectivity MRI
Wang, L., Su, L., Shen, H., & Hu, D. (2012) · PLoS ONE · doi:10.1371/journal.pone.0044530 · Cited by 115 · see citing works
Effects of weather and climate on the dynamics of animal population time series
Knape, J., & de Valpine, P. (2011) · Proceedings of the Royal Society B: Biological Sciences · doi:10.1098/rspb.2010.1333 · Cited by 107 · see citing works
Goswami, A., & Finarelli, J. A. (2016) · Evolution · doi:10.1111/evo.12956 · Cited by 99 · see citing works
Batalle, D., O'Muircheartaigh, J., Makropoulos, A., Kelly, C. J., Dimitrova, R., Hughes, E. J., Hajnal, J. V., Zhang, H., Alexander, D. C., Edwards, A. D., et al. (2019) · NeuroImage · doi:10.1016/j.neuroimage.2018.05.046 · Cited by 89 · see citing works
Changing expectations about speed alters perceived motion direction
Sotiropoulos, G., Seitz, A. R., & Seriès, P. (2011) · Current Biology · doi:10.1016/j.cub.2011.09.013 · Cited by 82 · see citing works
Effects of fire on spotted owl site occupancy in a late-successional forest
Roberts, S. L., van Wagtendonk, J. W., Miles, A. K., & Kelt, D. A. (2011) · Biological Conservation · doi:10.1016/j.biocon.2010.11.002 · Cited by 81 · see citing works
Mixture-based clustering for the ordered stereotype model
Fernández, D., Arnold, R., & Pledger, S. (2016) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2014.11.004 · Cited by 39 · see citing works
Pre- versus post-exercise protein intake has similar effects on muscular adaptations
Schoenfeld, B. J., Aragon, A., Wilborn, C., Urbina, S. L., Hayward, S. E., & Krieger, J. (2017) · PeerJ · doi:10.7717/peerj.2825 · Cited by 33 · see citing works
Bauer, J., Kirschbaum, M. U. F., Weihermüller, L., Huisman, J. A., Herbst, M., & Vereecken, H. (2008) · Soil Biology and Biochemistry · doi:10.1016/j.soilbio.2008.07.024 · Cited by 29 · see citing works
Nonconvergence, covariance constraints, and class enumeration in growth mixture models.
McNeish, D., Harring, J. R., & Bauer, D. J. (2023) · Psychological Methods · doi:10.1037/met0000456 · Cited by 27 · see citing works
School start times and teenage driver motor vehicle crashes
Foss, R. D., Smith, R. L., & O'Brien, N. P. (2019) · Accident Analysis & Prevention · doi:10.1016/j.aap.2018.03.031 · Cited by 17 · see citing works
Ridley, B. J., Cornelissen, P. L., Maalin, N., Mohamed, S., Kramer, R. S. S., McCarty, K., & Tovée, M. J. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.980277 · Cited by 15 · see citing works
Factor mixture modeling of intolerance of uncertainty.
Oglesby, M. E., Allan, N. P., Short, N. A., Raines, A. M., & Schmidt, N. B. (2017) · Psychological Assessment · doi:10.1037/pas0000357 · Cited by 15 · see citing works
Goertler, P. A. L., Scheuerell, M. D., Simenstad, C. A., & Bottom, D. L. (2016) · PLOS ONE · doi:10.1371/journal.pone.0162121 · Cited by 10 · see citing works
Colas, J. T., O’Doherty, J. P., & Grafton, S. T. (2024) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1011950 · Cited by 6 · see citing works
Rider, H. J., Morgan, K. M., Bond, A. T., Nolan, J. D., Fox, A. G., & Hamel, M. J. (2026) · Environmental Biology of Fishes · doi:10.1007/s10641-026-01901-0 · Cited by 1 · see citing works
River Otter Predation of Nesting Seabirds Along the Coasts of North America
Stuntz, L., & Orben, R. A. (2025) · Ecology and Evolution · doi:10.1002/ece3.72118
“We used an all-subsets model selection approach (due to the small model set), with Akaike's Corrected Information Criterion (AICc) as our selection criteria to account for our limited sample size (Hurvich and Tsai 1989).”
Tang, S., Li, Q., Liu, L., He, L., Zhang, Y., & Chen, L. (2026) · Journal of Nursing Management · doi:10.1155/jonm/8833031
- Authors
- HURVICH, C. M., & TSAI, C.-L.
- Affiliations
- New York University (US)
- University of California, Davis (US)
- ORCID
- HURVICH, CLIFFORD M.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1989
- Volume
- 76
- Issue
- 2
- Pages
- 297-307
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W1968371014
- Cited by
- 6,586
- References
- 1
- Citations by year
- 2026: 320 · 2025: 295 · 2024: 290 · 2023: 290 · 2022: 321 · 2021: 428 · 2020: 421 · 2019: 404 · 2018: 365 · 2017: 351 · 2016: 322 · 2015: 341 · 2014: 324 · 2013: 312 · 2012: 225
- FWCI
- 7.25
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrika (publishedVersion)
- Funders
- Innovative Research Group Project of the National Natural Science Foundation of China
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Keywords
- Akaike information criterion, AICc, bias correction, model selection, small sample size, regression models, autoregressive time series, model order selection, non-stationary time series, asymptotic efficiency
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review