Improving upon the effective sample size based on Godambe information for block likelihood inference. (English) Zbl 07876402
Summary: We consider the effective sample size, based on Godambe information, for block likelihood inference which is an attractive and computationally feasible alternative to full likelihood inference for large correlated datasets. With reference to a Gaussian random field having a constant mean, we explore how the choice of blocks impacts this effective sample size. This is done by introducing a column-wise blocking method which spreads out the spatial points within each block, instead of keeping them close together as the existing row-wise blocking method does. It is seen that column-wise blocking can lead to considerable gains in effective sample size and efficiency compared to row-wise blocking, while retaining computational simplicity. Analytical results in this direction are obtained under the AR (1) model. The insights so found facilitate the study of other one-dimensional correlation models as well as correlation models on a plane, where closed form expressions are intractable. Simulations are seen to provide support to our conclusions.
MSC:
| 62-08 | Computational methods for problems pertaining to statistics |
References:
| [1] | Acosta, J.; Alegría, A.; Osorio, F.; Vallejos, R., Assessing the effective sample size for large spatial datasets: a block likelihood approach, Comput Stat Data Anal, 162, 2021 · Zbl 07422761 · doi:10.1016/j.csda.2021.107282 |
| [2] | Acosta, J.; Vallejos, R., Effective sample size for spatial regression models, Electron J Stat, 12, 3147-3180, 2018 · Zbl 1407.62344 · doi:10.1214/18-EJS1460 |
| [3] | Bayley, GV; Hammersley, JM, The “effective” number of independent observations in an autocorrelated times series, J R Stat Soc Suppl, 8, 184-197, 1946 · Zbl 0063.00257 · doi:10.2307/2983560 |
| [4] | Berger, J.; Bayarri, MJ; Pericchi, LR, The effective sample size, Econom Rev, 33, 197-217, 2014 · Zbl 1491.62183 · doi:10.1080/07474938.2013.807157 |
| [5] | Bevilacqua, M.; Gaetan, C., Comparing composite likelihood methods based on pairs for spatial Gaussian random fields, Stat Comput, 25, 877-892, 2015 · Zbl 1332.62368 · doi:10.1007/s11222-014-9460-6 |
| [6] | Caragea, PC; Smith, RL, Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models, J Multivar Anal, 98, 1417-1440, 2007 · Zbl 1116.62101 · doi:10.1016/j.jmva.2006.08.010 |
| [7] | Chatterjee, S.; Diaconis, P., The sample size required in importance sampling, Ann Appl Probab, 28, 1099-1135, 2018 · Zbl 1391.65008 · doi:10.1214/17-AAP1326 |
| [8] | Datta, A.; Banerjee, S.; Finley, AO; Gelfand, AE, On nearest-neighbor Gaussian process models for massive spatial data, Wiley Interdiscip Rev Comput Stat, 8, 162-171, 2016 · Zbl 07912802 · doi:10.1002/wics.1383 |
| [9] | Faes, C.; Molenberghs, G.; Aerts, M.; Verbeke, G.; Kenward, M., The effective sample size and an alternative small-sample degrees-of-freedom method, Am Stat, 63, 389-399, 2009 · Zbl 1182.62098 · doi:10.1198/tast.2009.08196 |
| [10] | Godambe, VP; Kale, BK; Godambe, VP, Estimating functions: an overview, Estimating functions, 3-20, 1991, Oxford: Clarendon Press, Oxford · Zbl 0755.62027 · doi:10.1093/oso/9780198522287.003.0001 |
| [11] | Griffith, D., Effective geographic sample size in the presence of spatial autocorrelation, Ann Assoc Am Geogr, 95, 740-760, 2005 · doi:10.1111/j.1467-8306.2005.00484.x |
| [12] | Griffith, D., Geographic sampling of urban soils for contaminant mapping: how many samples and from where, Environ Geochem Hlth, 30, 495-509, 2008 · doi:10.1007/s10653-008-9186-5 |
| [13] | Martino, L.; Elvira, V.; Louzada, F., Effective sample size for importance sampling based on discrepancy measures, Signal Process, 131, 386-401, 2017 · doi:10.1016/j.sigpro.2016.08.025 |
| [14] | Vallejos, R.; Acosta, J., The effective sample size for multivariate spatial processes with an application to soil contamination, Nat Resour Model, 34, 2021 · doi:10.1111/nrm.12322 |
| [15] | Vallejos, R.; Osorio, F., Effective sample size of spatial process models, Spat Stat, 9, 66-92, 2014 · doi:10.1016/j.spasta.2014.03.003 |
| [16] | Varin, C.; Reid, N.; Firth, D., An overview of composite likelihood methods, Stat Sin, 21, 5-42, 2011 · Zbl 1534.62022 |
| [17] | Xu, G.; Genton, MG, Tukey g-and-h random fields, J Am Stat Assoc, 112, 1236-1249, 2017 · doi:10.1080/01621459.2016.1205501 |
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