×
de Carvalho, M.; Pereira, S.; Pereira, P.; de Zea Bermudez, P.

An extreme value Bayesian Lasso for the conditional left and right tails. (English) Zbl 07570501

J. Agric. Biol. Environ. Stat. 27, No. 2, 222-239 (2022).

Cited in 3 Documents

MSC:

62P12 Applications of statistics to environmental and related topics

Keywords:

conditional tail; extended generalized Pareto distribution; heavy-tailed response; Lasso; \(L_1\)-penalization; nonstationary extremes; statistics of extremes; variable selection

Software:

ismev; rjags; KernSmooth; Stan
Cite Review PDF
Full Text: DOI arXiv
OA License

References:

[1] Arnold, BC; Press, SJ, Bayesian estimation and prediction for Pareto data, J Am Stat Assoc, 84, 1079-1084 (1989) · Zbl 0702.62026 · doi:10.1080/01621459.1989.10478875
[2] Baioni, D.; Castaldini, D.; Cencetti, C., Human activity and damaging landslides and floods on Madeira Island, Nat Hazards Earth Syst Sci, 11, 3035-3046 (2011) · doi:10.5194/nhess-11-3035-2011
[3] Behrens, CN; Lopes, HF; Gamerman, D., Bayesian analysis of extreme events with threshold estimation, Stat Modell, 4, 227-244 (2004) · Zbl 1111.62023 · doi:10.1191/1471082X04st075oa
[4] Beirlant, J.; Goegebeur, Y.; Segers, J.; Teugels, J., Statistics of extremes: Theory and applications (2004), Hoboken: Wiley, Hoboken · Zbl 1070.62036 · doi:10.1002/0470012382
[5] Bhattacharya, A.; Pati, D.; Pillai, NS; Dunson, DB, Dirichlet-Laplace priors for optimal shrinkage, J Am Stat Assoc, 110, 1479-1490 (2015) · Zbl 1373.62368 · doi:10.1080/01621459.2014.960967
[6] Brown, SJ, The drivers of variability in UK extreme rainfall, Int J Climatol, 38, e119-e130 (2018) · doi:10.1002/joc.5356
[7] Cabras, S.; Castellanos, ME, A Bayesian approach for estimating extreme quantiles under a semiparametric mixture model, ASTIN Bull, 41, 87-106 (2011) · Zbl 1220.62056
[8] Carreau, J.; Bengio, Y., A hybrid Pareto model for asymmetric fat-tailed data: The univariate case, Extremes, 12, 53-76 (2009) · Zbl 1223.62030 · doi:10.1007/s10687-008-0068-0
[9] Carvalho, CM; Polson, NG; Scott, JG, The horseshoe estimator for sparse signals, Biometrika, 97, 465-480 (2010) · Zbl 1406.62021 · doi:10.1093/biomet/asq017
[10] Castellanos, ME; Cabras, S., A default Bayesian procedure for the generalized Pareto distribution, J Stat Plann Inference, 137, 473-483 (2007) · Zbl 1102.62023 · doi:10.1016/j.jspi.2006.01.006
[11] Chavez-Demoulin, V.; Davison, AC, Generalized additive modelling of sample extremes, J R Stat Soc Ser C (Appl Stat), 54, 207-222 (2005) · Zbl 1490.62194 · doi:10.1111/j.1467-9876.2005.00479.x
[12] Chavez-Demoulin, V.; Embrechts, P.; Hofert, M., An extreme value approach for modeling operational risk losses depending on covariates, J Risk Insur, 83, 735-776 (2016) · doi:10.1111/jori.12059
[13] Chernozhukov, V., Extremal quantile regression, Ann Stat, 33, 806-839 (2005) · Zbl 1068.62063 · doi:10.1214/009053604000001165
[14] Coles, S., An introduction to statistical modeling of extreme values (2001), London: Springer, London · Zbl 0980.62043 · doi:10.1007/978-1-4471-3675-0
[15] Davison, AC, Smith R L (1990), Models for exceedances over high thresholds (with Discussion). J R Stat Soc Ser B (Stat Methodol), 393-442 · Zbl 0706.62039
[16] de Zea Bermudez, P.; Kotz, S., Parameter estimation of the generalized Pareto distribution-Part II, J Stat Plann Inference, 140, 1374-1388 (2010) · Zbl 1190.62039 · doi:10.1016/j.jspi.2008.11.020
[17] de Zea Bermudez, P.; Turkman, MA, Bayesian approach to parameter estimation of the generalized Pareto distribution, Test, 12, 259-277 (2003) · Zbl 1039.62023 · doi:10.1007/BF02595822
[18] do Nascimento, F. F.; Gamerman, D.; Lopes, H. F., A semiparametric Bayesian approach to extreme value estimation, Stat Comput, 22, 661-675 (2012) · Zbl 1322.62049 · doi:10.1007/s11222-011-9270-z
[19] Dunn, PK; Smyth, GK, Randomized quantile residuals, J Comput Graph Stat, 5, 236-244 (1996)
[20] Eastoe, EF; Tawn, JA, Modelling non-stationary extremes with application to surface level ozone, J R Stat Soc Ser C (Appl Stat), 58, 25-45 (2009) · doi:10.1111/j.1467-9876.2008.00638.x
[21] Embrechts, P.; Klüppelberg, C.; Mikosch, T., Modelling extremal events for insurance and finance (1997), New York: Springer, New York · Zbl 0873.62116 · doi:10.1007/978-3-642-33483-2
[22] Fragoso, M.; Trigo, R.; Pinto, J.; Lopes, S.; Lopes, A.; Ulbrich, S.; Magro, C., The 20 February 2010 Madeira flash-floods: Synoptic analysis and extreme rainfall assessment, Nat Hazards Earth Syst Sci, 12, 715-730 (2012) · doi:10.5194/nhess-12-715-2012
[23] Frigessi, A.; Haug, O.; Rue, H., A dynamic mixture model for unsupervised tail estimation without threshold selection, Extremes, 5, 219-235 (2002) · Zbl 1039.62042 · doi:10.1023/A:1024072610684
[24] Geisser, S.; Eddy, WF, A predictive approach to model selection, J Am Stat Assoc, 74, 153-160 (1979) · Zbl 0401.62036 · doi:10.1080/01621459.1979.10481632
[25] Gelfand, AE; Dey, DK, Bayesian model choice: asymptotics and exact calculations, J R Stat Soc Ser B (Stat Methodol), 56, 501-514 (1994) · Zbl 0800.62170
[26] Gelman, A.; Lee, D.; Guo, J., Stan: A probabilistic programming language for Bayesian inference and optimization, J Edu Behav Stati, 40, 530-543 (2015) · doi:10.3102/1076998615606113
[27] George, EI; McCulloch, RE, Variable selection via Gibbs sampling, J Am Stat Assoc, 88, 881-889 (1993) · doi:10.1080/01621459.1993.10476353
[28] Ghosal, S.; Van der Vaart, AW, Fundamentals of nonparametric Bayesian inference (2015), Cambridge: Cambridge University Press, Cambridge · Zbl 1376.62004
[29] Groll, A.; Hambuckers, J.; Kneib, T.; Umlauf, N., LASSO-type penalization in the framework of generalized additive models for location, scale and shape, Comput Stat Data Anal, 140, 59-73 (2019) · Zbl 1496.62119 · doi:10.1016/j.csda.2019.06.005
[30] Huser, R.; Genton, MG, Non-stationary dependence structures for spatial extremes, J Agric Biol Environ Stat, 21, 470-491 (2016) · Zbl 1347.62246 · doi:10.1007/s13253-016-0247-4
[31] Kenyon, J.; Hegerl, GC, Influence of modes of climate variability on global precipitation extremes, J Climate, 23, 6248-6262 (2010) · doi:10.1175/2010JCLI3617.1
[32] Kleiber, C.; Kotz, S., Statistical size distributions in economics and actuarial sciences (2003), New York: Wiley, New York · Zbl 1044.62014 · doi:10.1002/0471457175
[33] Koenker, R., Quantile regression (2005), Cambridge: Cambridge University Press, Cambridge · Zbl 1111.62037 · doi:10.1017/CBO9780511754098
[34] Koenker R, Bassett G. (1978), Regression quantiles, Econometrica, 33-50 · Zbl 0373.62038
[35] MacDonald, A.; Scarrott, C.; Lee, D.; Darlow, B.; Reale, M.; Russell, G., A flexible extreme value mixture model, Comput Stat Data Anal, 55, 2137-2157 (2011) · Zbl 1328.62296 · doi:10.1016/j.csda.2011.01.005
[36] Mahmoud, MR; Abd El-Ghafour, AS, Fisher information matrix for the generalized Feller-Pareto distribution, Commun Stat Theory Methods, 44, 4396-4407 (2015) · Zbl 1352.62037 · doi:10.1080/03610926.2013.841933
[37] Naveau, P.; Huser, R.; Ribereau, P.; Hannart, A., Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection, Water Resour Res, 52, 2753-2769 (2016) · doi:10.1002/2015WR018552
[38] Olsen, MK; Schafer, JL, A two-part random-effects model for semicontinuous longitudinal data, J Am Stat Assoc, 96, 730-745 (2001) · Zbl 1017.62064 · doi:10.1198/016214501753168389
[39] Papastathopoulos, I.; Tawn, JA, Extended generalised Pareto models for tail estimation, J Stat Plann Inference, 143, 131-143 (2013) · Zbl 1251.62020 · doi:10.1016/j.jspi.2012.07.001
[40] Park, T.; Casella, G., The Bayesian Lasso, J Am Stat Assoc, 103, 681-686 (2008) · Zbl 1330.62292 · doi:10.1198/016214508000000337
[41] Petrone, S.; Wasserman, L., Consistency of Bernstein polynomial posteriors, J R Stat Soc Ser B (Stat Methodol), 64, 79-100 (2002) · Zbl 1015.62033 · doi:10.1111/1467-9868.00326
[42] Plummer M (2019), rjags: Bayesian graphical models using MCMC. R package version 4-10, http://CRAN.R-project.org/package=rjags
[43] Polson NG, Sokolov V (2019) Bayesian regularization: From Tikhonov to horseshoe. Computational Statistics, Wiley Interdisciplinary Reviews, p e1463 · Zbl 07909162
[44] Reich, BJ; Ghosh, SK, Bayesian statistical methods (2019), Boca Raton: Chapman & Hall/CRC, Boca Raton · Zbl 1427.62001 · doi:10.1201/9780429202292
[45] Resnick, SI, Tail equivalence and its applications, J Appl Probab, 8, 136-156 (1971) · Zbl 0217.49903 · doi:10.2307/3211844
[46] Santos, M.; Santos, JA; Fragoso, M., Atmospheric driving mechanisms of flash floods in Portugal, Int J Climatol, 37, 671-680 (2017) · doi:10.1002/joc.5030
[47] Schott, JR, Matrix analysis for statistics (2016), New York: Wiley, New York
[48] Stein ML (2020) Parametric models for distributions when interest is in extremes with an application to daily temperature, Extremes, 1-31
[49] Stein, ML, A parametric model for distributions with flexible behavior in both tails, Environmetrics, 32, e2658 (2021)
[50] Tencaliec P, Favre A-C, Naveau P, Prieur C, Nicolet G (2019) Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount. Environmetrics, e2582
[51] Tibshirani, R., Regression shrinkage and selection via the Lasso, J R Stat Soc Ser B (Stat Methodol), 58, 267-288 (1996) · Zbl 0850.62538
[52] Umlauf, N.; Kneib, T., A primer on Bayesian distributional regression, Stat Modell, 18, 219-247 (2018) · Zbl 07289507 · doi:10.1177/1471082X18759140
[53] Villa, C., Bayesian estimation of the threshold of a generalised Pareto distribution for heavy-tailed observations, Test, 26, 95-118 (2017) · Zbl 1422.62111 · doi:10.1007/s11749-016-0501-7
[54] Wand, MP; Jones, MC, Kernel smoothing (1995), London: Chapman & Hall, London · Zbl 0854.62043 · doi:10.1007/978-1-4899-4493-1
[55] Wang, H.; Tsai, C-L, Tail index regression, J Am Stat Assoc, 104, 1233-1240 (2009) · Zbl 1388.62145 · doi:10.1198/jasa.2009.tm08458
[56] Whan, K.; Zwiers, F., The impact of ENSO and the NAO on extreme winter precipitation in North America in observations and regional climate models, Climate Dyn, 48, 1401-1411 (2017) · doi:10.1007/s00382-016-3148-x
[57] Young, GA; Smith, RL, Essentials of statistical inference (2005), Cambridge: Cambridge University Press, Cambridge · Zbl 1087.62002 · doi:10.1017/CBO9780511755392
[58] Yuan, M.; Lin, Y., Model selection and estimation in regression with grouped variables, J R Stat Soc Ser B (Stat Methodol), 68, 49-67 (2006) · Zbl 1141.62030 · doi:10.1111/j.1467-9868.2005.00532.x
[59] Zhang, X.; Wang, J.; Zwiers, FW; Groisman, PY, The influence of large-scale climate variability on winter maximum daily precipitation over North America, J Climate, 23, 2902-2915 (2010) · doi:10.1175/2010JCLI3249.1
[60] Zhang Y. D, Naughton B. P, Bondell H. D, Reich B. J. (2020), Bayesian regression using a prior on the model fit: The R2-D2 shrinkage prior. J Am Stat Assoc 1-13
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.