150
Views
5
CrossRef citations to date
0
Altmetric
Articles

Improved robust model selection methods for a Lévy nonparametric regression in continuous time

ORCID Icon, ORCID Icon & ORCID Icon
Pages 612-628 | Received 27 Mar 2018, Accepted 15 Apr 2019, Published online: 26 Apr 2019

References

  • Akaike, H. (1974), ‘A New Look at the Statistical Model Identification’, IEEE Transactions on Automatic Control, 19, 716–723. doi: 10.1109/TAC.1974.1100705.
  • Barndorff-Nielsen, O.E., and Shephard, N. (2001), ‘Non-Gaussian Ornstein-Uhlenbeck-based Models and Some of Their Uses in Financial Economics’, Journal of the Royal Statistical Society: Series B, 63, 167–241. doi: 10.1111/1467-9868.00282.
  • Barron, A., Birgé, L., and Massart, P. (1999), ‘Risk Bounds for Model Selection Via Penalization’, Probability Theory and Related Fields, 113, 301–413. doi: 10.1007/s004400050210.
  • Bertoin, J. (1996), Lévy Processes, Cambridge: Cambridge University Press.
  • Comte, F., and Genon-Catalot, V. (2011), ‘Estimation for Lévy Processes From High Frequency Data Within a Long Time Interval’, The Annals of Statistics, 39, 803–837. doi: 10.1214/10-AOS856.
  • Cont, R., and Tankov, P. (2004), Financial Modelling with Jump Processes, London: Chapman & Hall.
  • Flaksman, A.G. (2002), ‘Adaptive Signal Processing in Antenna Arrays with Allowance for the Rank of the Impule-response Matrix of a Multipath Channel’, Radiophysics and Quantum Electronics, 45, 977–988. doi: 10.1023/A:1023585517419
  • Fourdrinier, D., and Pergamenshchikov, S. (2007), ‘Improved Model Selection Method for a Regression Function with Dependent Noise’, Annals of the Institute of Statistical Mathematics, 59, 435–464. doi: 10.1007/s10463-006-0063-7.
  • Fourdrinier, D., and Strawderman, W.E. (1996), ‘A Paradox Concerning Shrinkage Estimators: Should a Known Scale Parameter be Replaced by an Estimated Value in the Shrinkage Factor?’, Journal of Multivariate Analysis, 59, 109–140. doi: 10.1006/jmva.1996.0056.
  • Galtchouk, L.I., and Pergamenshchikov, S.M. (2006), ‘Asymptotically Efficient Estimates for Nonparametric Regression Models’, Statistics and Probability Letters, 76, 852–860. doi: 10.1016/j.spl.2005.10.017.
  • Galtchouk, L.I., and Pergamenshchikov, S.M. (2009a), ‘Sharp Non-asymptotic Oracle Inequalities for Non-parametric Heteroscedastic Regression Models’, Journal of Nonparametric Statistics, 21, 1–18. doi: 10.1080/10485250802504096.
  • Galtchouk, L., and Pergamenshchikov, S. (2009b), ‘Adaptive Asymptotically Efficient Estimation in Heteroscedastic Nonparametric Regression’, Journal of the Korean Statistical Society, 38, 305–322. doi:j.jkss.2008.12.001. doi: 10.1016/j.jkss.2008.12.001
  • Ibragimov, I.A., and Khasminskii, R.Z. (1981), Statistical Estimation: Asymptotic Theory, New York: Springer.
  • Jacod, J., and Shiryaev, A.N. (2002), Limit Theorems for Stochastic Processes (2nd ed.), Berlin: Springer.
  • James, W., and Stein, C. (1961), ‘Estimation with quadratic loss’, in Proceedings of the Fourth Berkeley Symposium Mathematics, Statistics and Probability, Berkeley: University of California Press, 1, pp. 361–380.
  • Kassam, S.A. (1988), Signal Detection in Non-Gaussian Noise, New York: Springer.
  • Konev, V.V., and Pergamenshchikov, S.M. (2009a), ‘Nonparametric Estimation in a Semimartingale Regression Model. Part 1. Oracle Inequalities’, Journal of Mathematics and Mechanics of Tomsk State University, 3, 23–41.
  • Konev, V.V., and Pergamenshchikov, S.M. (2009b), ‘Nonparametric Estimation in a Semimartingale Regression Model. Part 2. Robust Asymptotic Efficiency’, Journal of Mathematics and Mechanics of Tomsk State University, 4, 31–45.
  • Konev, V.V., and Pergamenshchikov, S.M. (2010), ‘General Model Selection Estimation of a Periodic Regression with a Gaussian Noise’, Annals of the Institute of Statistical Mathematics, 62, 1083–1111. doi: 10.1007/s10463-008-0193-1.
  • Konev, V.V., and Pergamenshchikov, S.M. (2012), ‘Efficient Robust Nonparametric Estimation in a Semimartingale Regression Model’, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 48, 1217–1244. doi: 10.1214/12-AIHP488.
  • Konev, V.V., and Pergamenshchikov, S.M. (2015), ‘Robust Model Selection for a Semimartingale Continuous Time Regression From Discrete Data’, Stochastic Processes and their Applications, 125, 294–326. doi: 10.1016/j.spa.2014.08.003.
  • Konev, V., Pergamenshchikov, S., and Pchelintsev, E. (2014), ‘Estimation of a Regression with the Pulse Type Noise From Discrete Data’, Theory of Probability & its Applications, 58, 442–457. doi: 10.1137/S0040585X9798662X.
  • Kutoyants, Yu.A. (1977), ‘Estimation of the Signal Parameter in a Gaussian Noise’, Problems of Information Transmission, 13, 29–36.
  • Kutoyants, Yu.A. (1984), Parameter Estimation for Stochastic Processes, Berlin: Heldeman-Verlag.
  • Mallows, C. (1973), ‘Some Comments on Cp’, Technometrics, 15, 661–675.
  • Nussbaum, M. (1985), ‘Spline Smoothing in Regression Models and Asymptotic Efficiency in L2’, The Annals of Statistics, 13, 984–997. doi: 10.1214/aos/1176349651.
  • Pchelintsev, E. (2013), ‘Improved Estimation in a Non-Gaussian Parametric Regression’, Statistical Inference for Stochastic Processes, 16, 15–28. doi: 10.1007/s11203-013-9075-0.
  • Pinsker, M.S. (1981), ‘Optimal Filtration of Square Integrable Signals in Gaussian White Noise’, Problems of Transimission Information, 17, 120–133.
  • Proakis, J.G. (1995), Digital Communications, New York: McGraw-Hill.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.