S. Arlot and P. Massart, Data-driven calibration of penalties for least-squares regression, J. Mach. Learn. Res, vol.10, p.245279, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00243116

J. Bai, Estimation of multiple-regime regressions with least absolutes deviation, Journal of Statistical Planning and Inference, vol.74, p.103134, 1998.

J. Bai and P. Perron, Estimating and testing linear models with multiple structural changes, Econometrica, vol.66, p.4778, 1998.

J. Bardet and C. Dion, Robust semi-parametric multiple change-point detection, Signal Processing, vol.11, p.156, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01846029

J. Bardet and A. Guenaizi, Data-driven semi-parametric detection of multiple changes in long-range dependent processes, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01676967

J. Bardet, W. Kengne, and O. Wintenberger, Multiple breaks detection in general causal time series using penalized quasi-likelihood, Electron. J. Statist, vol.6, p.435477, 2012.

J. Bardet and O. Wintenberger, Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes, Ann. Statist, vol.37, p.27302759, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00193955

M. Basseville and I. V. Nikiforov, Detection of Abrupt Changes: Theory and Application, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00008518

S. M. Berman, A compound Poisson limit for stationary sums, and sojourns of Gaussian processes, Ann. Probab, vol.8, issue.3, p.511538, 1980.

M. Birem, J. Quinton, F. Berry, and Y. Mezouar, Sail-map: Loop-closure detection using saliency-based features, IEEE/RSJ International Conference on Intelligent Robots and Systems, p.45434548, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01626473

V. Brault and J. Chiquet, blockseg: Two dimensional change-points detection, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02011057

V. Brault, J. Chiquet, and C. Lévy-leduc, Ecient block boundaries estimation in block-wise constant matrices: An application to hic data, Electron. J. Statist, vol.11, issue.1, p.15701599, 2017.

V. Brault, G. Cougoulat, S. Ouadah, and L. Sansonnet, Muchpoint: Multiple change point, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02011077

V. Brault, A. Leclercq-samson, and J. Quinton, Segmentation des lignes et des colonnes d'une matrice : application aux séquences de navigation visuelle, 49èmes Journées de Statistique, 2017.

V. Brault, S. Ouadah, L. Sansonnet, and C. Lévy-leduc, Nonparametric multiple change-point estimation for analyzing large hi-c data matrices, Journal of Multivariate Analysis, vol.165, pp.143-165, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01468198

V. Brault, A. Samson, and J. Quinton, Modélisation statistique pour détecter des séquences vidéos similaires : application aux véhicules autonomes, 2018.

B. E. Brodsky and B. S. Darkhovsky, Nonparametric methods in change-point problems, 1993.

K. S. Chan, Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model, Ann. Statist, vol.21, issue.1, p.520533, 1993.

K. S. Chan and H. Tong, On the use of the deterministic Lyapunov function for the ergodicity of stochastic dierence equations, Adv. in Appl. Probab, vol.17, issue.3, p.666678, 1985.

N. H. Chan and Y. A. Kutoyants, Recent developments of threshold estimation for nonlinear time series, J. Japan Statist. Soc, vol.40, issue.2, p.277303, 2010.

N. H. Chan and Y. A. Kutoyants, On parameter estimation of threshold autoregressive models, Stat. Inference Stoch. Process, vol.15, issue.1, p.81104, 2012.

H. Cherno and H. Rubin, The estimation of the location of a discontinuity in density, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol.I, p.1937, 1956.

O. V. Chernoyarov, S. Dachian, and Y. A. Kutoyants, On parameter estimation for cusp-type signals, Ann. Inst. Statist. Math, vol.70, issue.1, p.3962, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01741241

G. Ciuperca, Maximum likelihood estimator in a two-phase nonlinear random regression model, Statist. Decisions, vol.22, issue.4, pp.335-349, 2004.

M. Csörg® and L. Horváth, Limit theorems in change-point analysis, Wiley Series in Probability and Statistics, 1997.

S. Dachian, Estimation of cusp location by Poisson observations, Stat. Inference Stoch. Process, vol.6, issue.1, p.114, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00469714

S. Dachian, N. Kordzakhia, Y. Kutoyants, and A. Novikov, Estimation of cusp location of stochastic processes: a survey, Stat. Inference Stoch. Process, vol.21, issue.2, p.345362, 2018.

S. Dachian and Y. A. Kutoyants, On cusp estimation of ergodic diusion process, J. Statist. Plann. Inference, vol.117, issue.1, p.153166, 2003.

J. A. Davydov, The convergence of distributions which are generated by stationary random processes, Teor. Verojatnost. i Primenen, vol.13, p.730737, 1968.

J. R. Dixon, S. Selvaraj, F. Yue, A. Kim, Y. Li et al., Topological domains in mammalian genomes identied by analysis of chromatin interactions, Nature, vol.485, issue.7398, p.376380, 2012.

M. Döring, Asymmetric cusp estimation in regression models, Statistics, vol.49, issue.6, p.12791297, 2015.

M. Döring and U. Jensen, Smooth change point estimation in regression models with random design, Ann. Inst. Statist. Math, vol.67, issue.3, p.595619, 2015.

M. Elmi and B. Saussereau, Inference on threshold autoregressive models with dependent errors, 2018.

M. S. Ermakov, On the asymptotic behavior of statistical estimates for samples having a density with singularities, Theory Probab. Appl, vol.21, issue.3, p.649651, 1977.

C. Faure, J. Bardet, J. Lacaille, and M. Olteanu, Comparison of three algorithms for parametric change-point detection, Proceeding ESANN 2016, vol.04, p.2016

C. Francq and J. Zakoïan, Estimating linear representations of nonlinear processes, J. Statist. Plann. Inference, vol.68, issue.1, pp.145-165, 1998.

C. Francq and J. Zakoïan, GARCH Models: Structure, Statistical Inference and Financial Applications, 2010.

K. Frick, A. Munk, and H. Sieling, Multiscale change point inference, J. R. Stat. Soc. Ser. B. Stat. Methodol, vol.76, issue.3, p.495580, 2014.

P. Fryzlewicz, Wild binary segmentation for multiple change-point detection, Ann. Statist, vol.42, issue.6, p.22432281, 2014.

A. A. Gushchin and U. Küchler, On estimation of delay location, Stat. Inference Stoch. Process, vol.14, issue.3, p.273305, 2011.

B. E. Hansen, Inference in TAR models, Stud. Nonlinear Dyn. Econom, vol.2, issue.1, p.114, 1997.

B. E. Hansen, Sample splitting and threshold estimation, Econometrica, vol.68, issue.3, p.575603, 2000.

B. E. Hansen, Threshold autoregression in economics, Stat. Interface, vol.4, issue.2, p.123127, 2011.

Z. Harchaoui and C. Lévy-leduc, Multiple change-point estimation with a total variation penalty, Journal of the American Statistical Association, vol.105, issue.492, p.14801493, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00923474

R. Höpfner and Y. A. Kutoyants, On LAN for parametrized continuous periodic signals in a time inhomogeneous diusion, Statist. Decisions, vol.27, issue.4, p.309326, 2009.

I. A. Ibragimov and R. Z. Khasminskii, The asymptotic behavior of generalized Bayesian estimates, Dokl. Akad. Nauk SSSR, vol.194, issue.2, p.257260, 1970.

I. A. Ibragimov and R. Z. Khasminskii, Asymptotic behavior of statistical estimates for samples with a discontinuous density, Math. USSR-Sb, vol.16, issue.4, p.573606, 1972.

I. A. Ibragimov and R. Z. Khasminskii, The asymptotical behavior of location parameter statistical estimators for samples with continuous density with singularities, Zap. Nauchn. Sem. LOMI

I. A. Ibragimov and R. Z. Khasminskii, Parameter estimation for a discontinuous signal in white Gaussian noise, Probl. Inf. Transm, vol.11, issue.3, p.203212, 1975.

I. A. Ibragimov and R. Z. Khasminskii, Statistical estimation. Asymptotic theory, Applications of Mathematics, vol.16, 1981.

S. Kay, Fundamentals of statistical signal processing: detection theory, 1993.

N. E. Kordzakhia, Y. A. Kutoyants, A. A. Novikov, and L. Hin, On limit distributions of estimators in irregular statistical models and a new representation of fractional Brownian motion, Statist. Probab. Lett, vol.139, p.141151, 2018.

A. P. Korostelev and A. B. Tsybakov, Minimax Theory of Image Reconstruction, 1993.

H. Korrapati, J. Courbon, S. Alizon, and F. Marmoiton, the institut pascal data sets": un jeu de données en extérieur, multicapteurs et datées avec réalité terrain, données d'étalonnage et outils logiciels, Orasis, Congrès des jeunes chercheurs en vision par ordinateur, 2013.

H. L. Koul and L. Qian, Asymptotics of maximum likelihood estimator in a two-phase linear regression model, J. Statist. Plann. Inference, vol.108, issue.1

U. Küchler and Y. A. Kutoyants, Delay estimation for some stationary diusion-type processes, Scand. J. Statist, vol.27, issue.3, pp.405-414, 2000.

Y. A. Kutoyants, Parameter estimation for stochastic processes, Research and Exposition in Mathematics. Heldermann Verlag, vol.6, 1984.

Y. A. Kutoyants, Identication of dynamical systems with small noise, Mathematics and its Applications, vol.300, 1994.

Y. A. Kutoyants, Statistical inference for spatial Poisson processes, Lecture Notes in Statistics, vol.134, 1998.

Y. A. Kutoyants, Statistical inference for ergodic diusion processes, Springer Series in Statistics, 2004.

Y. A. Kutoyants, On cusp location estimation for perturbed dynamical system, Scand. J. Stat, 2019.

M. Lavielle and E. Moulines, Least-squares estimation of an unknown number of shifts in time series, Journal of Time Series Analysis, vol.21, pp.33-59, 2000.

E. Lebarbier, Detecting multiple change-points in the mean of gaussian process by model selection, Signal Process, vol.85, issue.4, pp.717-736, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00071847

D. Li, S. Ling, and W. K. Li, Asymptotic theory on the least squares estimation of threshold moving-average models, Econometric Theory, vol.29, issue.3, p.482516, 2013.

S. Ling and H. Tong, Testing for a linear MA model against threshold MA models, Ann. Statist, vol.33, issue.6, p.25292552, 2005.

R. S. Liptser and A. N. Shiryaev, Statistics of random processes, Applications of Mathematics, vol.6, 2001.

A. Lung-yut-fong, C. Lévy-leduc, and O. Cappé, Homogeneity and change-point detection tests for multivariate data using rank statistics, Journal de la Société Française de Statistique, vol.156, issue.4, p.133162, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00607410

J. Neveu, Mathematical foundations of the calculus of probability. Translated by Amiel Feinstein, 1965.

A. Novikov, N. Kordzakhia, and T. Ling, On moments of Pitman estimators: the case of fractional Brownian motion, Theory Probab. Appl, vol.58, issue.4, p.601614, 2014.

J. D. Petruccelli, On the consistency of least squares estimators for a threshold AR(1) model, J. Time Ser. Anal, vol.7, issue.4, p.269278, 1986.

J. D. Petruccelli and S. W. Woolford, A threshold AR(1) model, J. Appl. Probab, vol.21, issue.2, p.270286, 1984.

B. L. Rao, Estimation of the location of the cusp of a continuous density, Ann. Math. Statist, vol.39, issue.1, p.7687, 1968.

B. L. Rao, Estimation of cusp in nonregular nonlinear regression models, J. Multivariate Anal, vol.88, issue.2, p.243251, 2004.

L. Qian, On maximum likelihood estimators for a threshold autoregression, J. Statist. Plann. Inference, vol.75, issue.1, p.2146, 1998.

P. M. Robinson, Gaussian semiparametric estimation of long range dependence, Ann. Statist, vol.23, issue.5, p.16301661, 1995.

E. Seijo and B. Sen, Change-point in stochastic design regression and the bootstrap, Ann. Statist, vol.39, issue.3, p.15801607, 2011.

E. Seijo and B. Sen, A continuous mapping theorem for the smallest argmax functional, Electron. J. Stat, vol.5, p.421439, 2011.

H. Tong, Threshold models in nonlinear time series analysis, Lecture Notes in Statistics, vol.21, 1983.

H. Tong, A dynamical system approach, With an appendix by, Oxford Statistical Science Series, vol.6, 1990.

R. S. Tsay, Testing and modeling threshold autoregressive processes, J. Amer. Statist. Assoc, vol.84, issue.405, p.231240, 1989.

L. Vostrikova, Detecting`disorder' in multidimensional random processes, Soviet Math. Dokl, vol.24, p.5559, 1981.