K. Aarssen and L. De-haan, On the maximal life span of humans, Mathematical Population Studies, vol.1, issue.4, pp.259-281, 1994.
DOI : 10.1214/aos/1176343003

M. Abramovitz and I. Stegun, Handbook of Mathematical Functions, 1965.

E. Alvarado, D. V. Sandberg, and S. G. Pickford, Modeling large forest fires as extreme events, Northwest Sci, vol.72, pp.66-75, 1998.

Y. Aragon, A. Daouia, and C. Thomas-agnan, NONPARAMETRIC FRONTIER ESTIMATION: A CONDITIONAL QUANTILE-BASED APPROACH, Econometric Theory, vol.56, issue.02, pp.358-389, 2005.
DOI : 10.2307/2533009
URL : https://hal.archives-ouvertes.fr/hal-00078775

S. Asmussen, Risk theory in a Markovian environment, Scand. Actuar. J, vol.2, pp.69-100, 1989.

S. Asmussen, Ruin probabilities, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00569254

K. B. Athreya and J. Fukuchi, Confidence intervals for endpoints of a c, 1997.

A. Balkema and L. De-haan, Residual Life Time at Great Age, The Annals of Probability, vol.2, issue.5, pp.792-804, 1974.
DOI : 10.1214/aop/1176996548

L. E. Baum and T. Petrie, Statistical Inference for Probabilistic Functions of Finite State Markov Chains, The Annals of Mathematical Statistics, vol.37, issue.6, pp.1554-1563, 1966.
DOI : 10.1214/aoms/1177699147

L. E. Baum, T. Petrie, G. Soules, and N. Weiss, A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains, The Annals of Mathematical Statistics, vol.41, issue.1, pp.164-171, 1970.
DOI : 10.1214/aoms/1177697196

P. J. Bickel, Y. Ritov, and T. Rydén, Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models, The Annals of Statistics, vol.26, issue.4, pp.1614-1635, 1998.
DOI : 10.1214/aos/1024691255

P. Billingsley, N. H. Bingham, C. M. Goldie, and J. L. Teugels, Probability and measure Regular Variation, 1979.

T. Buch-larsen, J. P. Nielsen, M. Guillén, and C. Bolancé, Kernel density estimation for heavy-tailed distributions using the champernowne transformation, Statistics, vol.53, issue.6, pp.503-518, 2005.
DOI : 10.1080/02331880500439782

J. Cai and K. S. Tan, Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures, ASTIN Bulletin, vol.30, issue.01, pp.93-112, 2007.
DOI : 10.1111/1467-9965.00068

A. Caliebe, Properties of the maximum a posteriori path estimator in hidden Markov models, IEEE Transactions on Information Theory, vol.52, issue.1, pp.41-51, 2006.
DOI : 10.1109/TIT.2005.860425

O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models, 2005.

C. Cazals, J. Florens, and L. Simar, Nonparametric frontier estimation: a robust approach, Journal of Econometrics, vol.106, issue.1, pp.1-25, 2002.
DOI : 10.1016/S0304-4076(01)00080-X
URL : http://publications.ut-capitole.fr/1484/1/nonparametric.pdf

D. G. Champernowne, The theory of income distribution, Econometrica, vol.5, issue.4, pp.379-381, 1937.

D. G. Champernowne, The Graduation of Income Distributions, Econometrica, vol.20, issue.4, pp.591-615, 1952.
DOI : 10.2307/1907644

A. Chiragiev and Z. Landsman, Multivariate Pareto portfolios: TCE-based capital allocation and divided differences, Scandinavian Actuarial Journal, vol.7, issue.4, pp.261-280, 2007.
DOI : 10.1214/aos/1176343003

Y. S. Chow and H. Teicher, Probability Theory, 1997.

G. A. Churchill, Stochastic models for heterogeneous DNA sequences, Bulletin of Mathematical Biology, vol.45, issue.1, pp.79-94, 1989.
DOI : 10.1007/BF02458837

C. ¸-inlar and E. , Introduction to stochastic processes, 1975.

P. Cooke, Statistical inference for bounds of random variables, Biometrika, vol.66, issue.2, pp.367-374, 1979.
DOI : 10.1093/biomet/66.2.367

A. Daouia and L. Simar, Robust nonparametric estimators of monotone boundaries, Journal of Multivariate Analysis, vol.96, issue.2, pp.311-331, 2005.
DOI : 10.1016/j.jmva.2004.10.005
URL : http://doi.org/10.1016/j.jmva.2004.10.005

A. C. Davison and N. I. Ramesh, A stochastic model for times of exposures to air pollution from a point source, Statistics for the environment, 1993.

A. L. Dekkers, J. H. Einmahl, and L. De-haan, A Moment Estimator for the Index of an Extreme-Value Distribution, The Annals of Statistics, vol.17, issue.4, pp.1833-1855, 1989.
DOI : 10.1214/aos/1176347397

A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. Roy. Statist. Soc. Ser. B, vol.39, issue.1, pp.1-38, 1977.

L. Deng and J. W. Mark, Parameter estimation for Markov modulated Poisson processes via the EM algorithm with time discretization, Telecommunication Systems, vol.6, issue.1, pp.321-338, 1993.
DOI : 10.1007/BF02136167

D. Deprins, L. Simar, and H. Tulkens, Measuring labor efficiency in post offices The Performance of Public Enterprises: Concepts and Measurements, 1984.

J. Diebolt, A. Guillou, and I. Rached, A new look at probability-weighted moments estimators, Comptes Rendus Mathematique, vol.338, issue.8, pp.629-634, 2004.
DOI : 10.1016/j.crma.2004.02.011

J. Diebolt, A. Guillou, and I. Rached, Approximation of the distribution of excesses through a generalized probability-weighted moments method, Journal of Statistical Planning and Inference, vol.137, issue.3, pp.841-857, 2007.
DOI : 10.1016/j.jspi.2006.06.012
URL : https://hal.archives-ouvertes.fr/hal-00693666

H. Drees, A. Ferreira, and L. De-haan, On maximum likelihood estimation of the extreme value index, Ann. Appl. Probab, vol.14, issue.3, pp.1179-1201, 2004.

M. J. Farrell, The Measurement of Productive Efficiency, Journal of the Royal Statistical Society. Series A (General), vol.120, issue.3, pp.253-281, 1957.
DOI : 10.2307/2343100

F. Ferraty and P. Vieu, Nonparametric modelling for functional data, 2005.

R. A. Fisher and L. H. Tippett, Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proc. Camb, pp.180-190, 1928.
DOI : 10.1017/S0305004100015681

L. Gardes, Estimating the support of a Poisson process via the Faber-Schauder basis and extreme values, Publ. Inst. Statist, pp.43-72, 2002.

J. Geffroy, Sur unprobì eme d'estimation géométrique, Publ. Inst. Statist. Univ. Paris XIII, pp.191-210, 1964.

I. Gijbels, E. Mammen, B. U. Park, and L. Simar, On Estimation of Monotone and Concave Frontier Functions, Journal of the American Statistical Association, vol.84, issue.1, pp.94220-228, 1999.
DOI : 10.1287/mnsc.44.1.49

S. Girard, A. Iouditski, and A. Nazin, L 1-Optimal Nonparametric Frontier Estimation via Linear Programming, Automation and Remote Control, vol.46, issue.3, pp.2000-2018, 2005.
DOI : 10.1007/s10513-005-0231-x

S. Girard and P. Jacob, Extreme values and Haar series estimates of point process boundaries . Scand, J. Stat, vol.30, issue.2, pp.369-384, 2003.

S. Girard and P. Jacob, Projection estimates of point processes boundaries, Journal of Statistical Planning and Inference, vol.116, issue.1, 2003.
DOI : 10.1016/S0378-3758(02)00182-9

S. Girard and P. Jacob, Extreme values and kernel estimates of point processes boundaries, ESAIM: Probability and Statistics, vol.8, pp.150-168, 2004.
DOI : 10.1051/ps:2004008

S. Girard and P. Jacob, Frontier estimation via kernel regression on high power-transformed data, Journal of Multivariate Analysis, vol.99, issue.3, pp.403-420, 2008.
DOI : 10.1016/j.jmva.2006.11.006
URL : https://hal.archives-ouvertes.fr/hal-00077683

S. Girard and P. Jacob, Frontier estimation with local polynomials and high power-transformed data, Journal of Multivariate Analysis, vol.100, issue.8, pp.1691-1705, 2009.
DOI : 10.1016/j.jmva.2009.01.011
URL : https://hal.archives-ouvertes.fr/hal-00384731

S. Girard and L. Menneteau, Central limit theorems for smoothed extreme value estimates of Poisson point processes boundaries, Journal of Statistical Planning and Inference, vol.135, issue.2, pp.433-460, 2005.
DOI : 10.1016/j.jspi.2004.04.020

B. V. Gnedenko, Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire, The Annals of Mathematics, vol.44, issue.3, 1943.
DOI : 10.2307/1968974

A. Goldenshluger and A. Tsybakov, Estimating the endpoint of a distribution in the presence of additive observation errors, Statistics & Probability Letters, vol.68, issue.1, pp.39-49, 2004.
DOI : 10.1016/j.spl.2004.01.013
URL : https://hal.archives-ouvertes.fr/hal-00103442

J. Grandell, Doubly stochastic Poisson processes, 1976.
DOI : 10.1007/BFb0077758

J. A. Greenwood, J. M. Landwehr, N. C. Matalas, and J. R. Wallis, Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form, Water Resources Research, vol.17, issue.2, pp.1049-1054, 1979.
DOI : 10.1029/WR015i005p01049

A. Guillou, S. Loisel, and G. Stupfler, Asymptotic normality of the maximum likelihood estimator of a loss process, 2011.

R. Gusella, Characterizing the variability of arrival processes with indexes of dispersion, IEEE Journal on Selected Areas in Communications, vol.9, issue.2, pp.203-211, 1991.
DOI : 10.1109/49.68448

L. De-haan, On Regular Variation and Its Applications to the Weak Convergence of Sample Extremes, Mathematical Centre Tract Mathematics Centre, vol.32, 1970.

L. De-haan, Estimation of the Minimum of a Function Using Order Statistics, Journal of the American Statistical Association, vol.73, issue.374, pp.467-469, 1981.
DOI : 10.1080/01621459.1981.10477669

L. De-haan and A. Ferreira, Extreme Value Theory, 2006.
DOI : 10.1007/0-387-34471-3

P. Hall, On Estimating the Endpoint of a Distribution, The Annals of Statistics, vol.10, issue.2, pp.556-568, 1982.
DOI : 10.1214/aos/1176345796

P. Hall and B. U. Park, Bandwidth choice for local polynomial estimation of smooth boundaries, Journal of Multivariate Analysis, vol.91, issue.2, pp.240-261, 2004.
DOI : 10.1016/j.jmva.2003.10.002

P. Hall, B. U. Park, and S. E. Stern, On Polynomial Estimators of Frontiers and Boundaries, Journal of Multivariate Analysis, vol.66, issue.1, 1998.
DOI : 10.1006/jmva.1998.1738

P. Hall and J. Z. Wang, Estimating the End-Point of a Probability Distribution Using Minimum-Distance Methods, Bernoulli, vol.5, issue.1, pp.177-189, 1999.
DOI : 10.2307/3318618

P. Hall and J. Z. Wang, Bayesian likelihood methods for estimating the end point of a distribution, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.2, issue.5, pp.717-729, 2005.
DOI : 10.1111/1468-0262.00455

W. Härdle, B. U. Park, and A. Tsybakov, Estimation of Non-sharp Support Boundaries, Journal of Multivariate Analysis, vol.55, issue.2, 1995.
DOI : 10.1006/jmva.1995.1075

H. Heffes and D. Lucantoni, A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance, IEEE Journal on Selected Areas in Communications, vol.4, issue.6, pp.856-867, 1986.
DOI : 10.1109/JSAC.1986.1146393

B. M. Hill, A Simple General Approach to Inference About the Tail of a Distribution, The Annals of Statistics, vol.3, issue.5, 1975.
DOI : 10.1214/aos/1176343247

U. Holst and G. Lindgren, Recursive estimation of parameters in Markov-modulated Poisson processes, IEEE Trans. Commun, issue.11, pp.432812-2820, 1995.

J. R. Hosking and J. R. Wallis, Parameter and Quantile Estimation for the Generalized Pareto Distribution, Technometrics, vol.4, issue.3, pp.339-349, 1987.
DOI : 10.1016/0022-1694(85)90108-8

P. Jacob and C. Suquet, Estimating the edge of a Poisson process by orthogonal series, Journal of Statistical Planning and Inference, vol.46, issue.2, 1995.
DOI : 10.1016/0378-3758(94)00103-3

B. H. Juang and L. R. Rabiner, Hidden Markov Models for Speech Recognition, Technometrics, vol.50, issue.4, pp.251-272, 1991.
DOI : 10.1007/978-3-642-66286-7

K. Kawashima and H. Saito, Teletraffic issues in ATM networks, Comp. Networks ISDN Sys, pp.369-375, 1990.
DOI : 10.1016/0169-7552(90)90046-U

S. Kim, N. Shephard, and S. Chib, Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models, Review of Economic Studies, vol.65, issue.3, pp.361-394, 1998.
DOI : 10.1111/1467-937X.00050
URL : http://restud.oxfordjournals.org/cgi/content/short/65/3/361

J. F. Kingman, Subadditive processes, in Ecole d'Eté de Probabilités de Saint-Flour V-1975, Lecture Notes in Mathematics, vol.539, 1976.

S. A. Klugman, H. H. Panjer, and G. E. Willmot, Loss models, 2004.

K. Knight, Limiting distributions of linear programming estimators, pp.87-103, 2001.

A. Korostelev, L. Simar, and A. Tsybakov, Efficient Estimation of Monotone Boundaries, The Annals of Statistics, vol.23, issue.2, 1995.
DOI : 10.1214/aos/1176324531

A. Korostelev and A. Tsybakov, Minimax theory of image reconstruction, Lecture Notes in Statistics, vol.82, 1993.
DOI : 10.1007/978-1-4612-2712-0

B. G. Leroux, Maximum-likelihood estimation for hidden Markov models. Stochastic Process, Appl, vol.40, pp.127-143, 1992.

D. Li and L. Peng, Does bias reduction with external estimator of second order parameter work for endpoint?, Journal of Statistical Planning and Inference, vol.139, issue.6, pp.1937-1952, 2009.
DOI : 10.1016/j.jspi.2008.08.023

F. Lindskog and A. Mcneil, Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling, ASTIN Bulletin, vol.L, issue.02, pp.209-238, 2003.
DOI : 10.1006/jmva.2000.1906

W. Y. Loh, Estimating an Endpoint of a Distribution with Resampling Methods, The Annals of Statistics, vol.12, issue.4, pp.1543-1550, 1984.
DOI : 10.1214/aos/1176346811

S. Loisel, Ruin theory with K lines of business, Proceedings of the 3rd Actuarial and Financial Day, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00379417

S. Loisel and X. Milhaud, From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital, European Journal of Operational Research, vol.214, issue.2, 2011.
DOI : 10.1016/j.ejor.2011.04.038
URL : https://hal.archives-ouvertes.fr/hal-00502847

G. J. Mclachlan and T. Krishnan, The EM Algorithm and Extensions, 1997.

K. S. Meier-hellstern, A fitting algorithm for Markov-modulated poisson processes having two arrival rates, European Journal of Operational Research, vol.29, issue.3, pp.970-977, 1987.
DOI : 10.1016/0377-2217(87)90250-5

L. Menneteau, Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries, ESAIM: Probability and Statistics, vol.12, pp.273-307, 2008.
DOI : 10.1051/ps:2007039

X. Milhaud, S. Loisel, and V. Maume-deschamps, Surrender triggers in life insurance: classification and risk predictions, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00509874

R. G. Miller, A Trustworthy Jackknife, The Annals of Mathematical Statistics, vol.35, issue.4, pp.1594-1605, 1964.
DOI : 10.1214/aoms/1177700384

C. Neves and A. Pereira, Detecting finiteness in the right endpoint of light-tailed distributions, Statistics & Probability Letters, vol.80, issue.5-6, pp.437-444, 2010.
DOI : 10.1016/j.spl.2009.11.021
URL : https://hal.archives-ouvertes.fr/hal-00612018

E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

J. Pickands, Statistical inference using extreme order statistics, Ann. Statist, vol.3, issue.1, pp.119-131, 1975.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, 1989.

D. S. Robson and J. H. Whitlock, Estimation of a truncation point, Biometrika, vol.51, issue.1-2, pp.33-39, 1964.
DOI : 10.1093/biomet/51.1-2.33

T. Rolski, H. Schmidli, V. Schmidt, and J. Teugels, Stochastic Processes for Insurance and Finance, 1999.
DOI : 10.1002/9780470317044

M. Rosenblatt, Remarks on Some Nonparametric Estimates of a Density Function, The Annals of Mathematical Statistics, vol.27, issue.3, pp.832-837, 1956.
DOI : 10.1214/aoms/1177728190

M. H. Rossiter, Characterizing a random point process by a switched Poisson process, 1989.

T. Rydén, Parameter estimation for Markov modulated poisson processes, Communications in Statistics. Stochastic Models, vol.73, issue.4, 1994.
DOI : 10.1109/TPAMI.1984.4767581

T. Rydén, Consistent and Asymptotically Normal Parameter Estimates for Hidden Markov Models, The Annals of Statistics, vol.22, issue.4, pp.1884-1895, 1994.
DOI : 10.1214/aos/1176325762

T. Rydén, Consistent and asymptotically normal parameter estimates for Markov modulated Poisson processes. Scand, J. Stat, vol.22, issue.3, pp.295-303, 1995.

T. Rydén, An EM algorithm for estimation in Markov-modulated Poisson processes, Computational Statistics & Data Analysis, vol.21, issue.4, pp.431-447, 1996.
DOI : 10.1016/0167-9473(95)00025-9

J. A. Smith, Statistical modeling of daily rainfall occurrences, Water Resources Research, vol.18, issue.5, pp.885-893, 1987.
DOI : 10.1029/WR023i005p00885

R. L. Smith, Estimating Tails of Probability Distributions, The Annals of Statistics, vol.15, issue.3, pp.1174-1207, 1987.
DOI : 10.1214/aos/1176350499

F. G. Tricomi and A. Erdélyi, The asymptotic expansion of a ratio of gamma functions, Pacific Journal of Mathematics, vol.1, issue.1, pp.133-142, 1951.
DOI : 10.2140/pjm.1951.1.133

P. Vandekerkhove, Consistent and asymptotically normal parameter estimates for hidden Markov mixtures of Markov models, Bernoulli, vol.11, issue.1, pp.103-129, 2005.
DOI : 10.3150/bj/1110228244
URL : https://hal.archives-ouvertes.fr/hal-00693110

A. Viterbi, Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE Transactions on Information Theory, vol.13, issue.2, pp.260-269, 1967.
DOI : 10.1109/TIT.1967.1054010