Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach

Bee, Marco; Hambuckers, Julien; Santi, Flavio; Trapin, Luca

doi:10.1007/s00180-021-01078-3

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Article (Scientific journals)

Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach

Bee, Marco; Hambuckers, Julien; Santi, Flavio et al.

2021 • In Computational Statistics, 36, p. 2177–2200

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/255714

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10.1007/s00180-021-01078-3

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Keywords :

Likelihood ratio; skewness; kurtosis; value-at-risk

Abstract :

[en] We develop a likelihood-ratio test for discriminating between the g-and-h and the g distribution, which is a special case of the former obtained when the parameter h is equal to zero. The g distribution is a shifted lognormal, and is therefore suitable for modeling economic and financial quantities. The g-and-h is a more flexible distribution, capable of fitting highly skewed and/or leptokurtic data, but is computationally much more demanding. Accordingly, in practical applications the test is a valuable tool for resolving the tractability-flexibility trade-off between the two distributions. Since the classical result for the asymptotic distribution of the test is not valid in this setup, we derive the null distribution via simulation. Further Monte Carlo experiments allow us to estimate the power function and to perform a comparison with a similar test proposed by Xu and Genton (2015). Finally, the practical relevance of the test is illustrated by two risk management applications dealing with operational and actuarial losses.

Research center :

HEC Recherche - HEC Recherche

Disciplines :

Quantitative methods in economics & management

Author, co-author :

Bee, Marco; University of Trento

Hambuckers, Julien ; Université de Liège - ULiège > HEC Liège : UER > UER Finance et Droit : Finance de Marché

Santi, Flavio; University of Verona

Trapin, Luca; University of Bologna

Language :

English

Title :

Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach

Publication date :

2021

Journal title :

Computational Statistics

ISSN :

0943-4062

eISSN :

1613-9658

Publisher :

Springer, Heidelberg, Germany

Volume :

Pages :

2177–2200

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

BNB - Banque Nationale de Belgique [BE]

Available on ORBi :

since 24 January 2021

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Bibliography

Bee M, Trapin L (2016) A simple approach to the estimation of Tukey’s gh distribution. J Stat Comput Simul 86(16):3287–3302 DOI: 10.1080/00949655.2016.1164159
Bee M, Hambuckers J, Trapin L (2019a) Estimating value-at-risk for the g-and-h distribution: an indirect inference approach. Quant Finance 19(8):1255–1266 DOI: 10.1080/14697688.2019.1580762
Bee M, Hambuckers J, Trapin L (2019b) An improved approach for estimating large losses in insurance analytics and operational risk using the g-and-h distribution. DEM working papers 2019/11
Byrd RH, Lu P, Nocedal J, Zhu C (1995) A limited memory algorithm for bound constrained optimization. SIAM J Sci Comput 16(5):1190–1208 DOI: 10.1137/0916069
Clementi F, Gallegati M (2005) Pareto’s law of income distribution: evidence for Germany, the United Kingdom, and the United States. In: Yarlagadda S, Chakrabarti B, Chatterjee A (eds) Econophysics of wealth distributions. Springer, Berlin, pp 3–14 DOI: 10.1007/88-470-0389-X_1
Cramér H (1946) Mathematical methods of statistics. Princeton University Press, Princeton
Cruz M, Peters G, Shevchenko P (2015) Fundamental aspects of operational risk and insurance analytics: a handbook of operational risk. Wiley, Hoboken DOI: 10.1002/9781118573013
Degen M, Embrechts P, Lambrigger DD (2007) The quantitative modeling of operational risk: between g-and-h and EVT. Astin Bull 37(2):265–291 DOI: 10.1017/S0515036100014860
Drovandi CC, Pettitt AN (2011) Likelihood-free Bayesian estimation of multivariate quantile distributions. Comput Stat Data Anal 55(9):2541–2556 DOI: 10.1016/j.csda.2011.03.019
Dupuis D, Field C (2004) Large wind speeds: modeling and outlier detection. J Agric Biol Environ Stat 9(1):105–121 DOI: 10.1198/1085711043163
Dutta KK, Babbel DF (2002) On measuring skewness and kurtosis in short rate distributions: the case of the US dollar London inter bank offer rates. Wharton School Center for Financial Institutions, University of Pennsylvania 02-25
Dutta KK, Perry J (2006) A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital. Technical Report 06-13, Federal Reserve Bank of Boston
Field C, Genton MG (2006) The multivariate g-and-h distribution. Technometrics 48(1):104–111 DOI: 10.1198/004017005000000562
Fischer M, Horn A, Klein I (2007) Tukey-type distributions in the context of financial data. Commun Stat Theory Methods 36(1):23–35 DOI: 10.1080/03610920500476382
Gibrat R (1931) Les Inégalités Économiques. Sirey, Paris
Groll A, Hambuckers J, Kneib T, Umlauf N (2019) Lasso-type penalization in the framework of generalized additive models for location, scale and shape. Comput Stat Data Anal 140:59–73 DOI: 10.1016/j.csda.2019.06.005
Hambuckers J, Groll A, Kneib T (2018) Understanding the economic determinants of the severity of operational losses: a regularized Generalized Pareto regression approach. J Appl Econom 33(6):898–935 DOI: 10.1002/jae.2638
Hoaglin DC (1985) Summarizing shape numerically: the g-and-h distributions, vol 11. Wiley, Hoboken, pp 461–513
Jiménez JA, Arunachalam V (2011) Using Tukey’s g and h family of distributions to calculate value-at-risk and conditional value-at-risk. J Risk 13(4):95–116 DOI: 10.21314/JOR.2011.230
Kleiber C, Kotz S (2003) Statistical size distributions in economics and actuarial sciences. Wiley, Hoboken DOI: 10.1002/0471457175
McDonald JB, Sorensen J, Turley PA (2013) Skewness and kurtosis properties of income distribution models. Rev Income Wealth 59(2):360–374 DOI: 10.1111/j.1475-4991.2011.00478.x
McNeil A, Frey R, Embrechts P (2015) Quantitative risk management: concepts, techniques, tools, 2nd edn. Princeton University Press, Princeton
Peters GW, Sisson S (2006) Bayesian inference, Monte Carlo sampling and operational risk. J Oper Risk 1(3):27–50 DOI: 10.21314/JOP.2006.014
Peters GW, Chen WY, Gerlach RH (2016) Estimating quantile families of loss distributions for non-life insurance modelling via L-moments. Risks 4(2):14 DOI: 10.3390/risks4020014
Prangle D (2017) gk: an R Package for the g-and-k and generalised g-and-h distributions. arXiv e-prints 1706.06889v1
Rayner GD, MacGillivray HL (2002) Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions. Stat Comput 12(1):57–75 DOI: 10.1023/A:1013120305780
Self SG, Liang KY (1987) Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J Am Stat Assoc 82(398):605–610 DOI: 10.1080/01621459.1987.10478472
Tukey JW (1977) Modern techniques in data analysis. In: NSF-sponsored regional research conference at Southern Massachusetts University, North Dartmouth
Wolny-Dominiak A, Trzesiok M (2014) insuranceData: a collection of insurance datasets useful in risk classification in non-life insurance. R package version 1.0
Xu G, Genton MG (2015) Efficient maximum approximated likelihood inference for Tukey’s g-and-h distribution. Comput Stat Data Anal 91:78–91 DOI: 10.1016/j.csda.2015.06.002
Xu G, Genton MG (2017) Tukey g-and-h random fields. J Am Stat Assoc 112(519):1236–1249 DOI: 10.1080/01621459.2016.1205501