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Adaptive Lasso-Type Estimation For Multivariate Diffusion Processes

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  • De Gregorio, Alessandro
  • Iacus, Stefano M.

Abstract

The least absolute shrinkage and selection operator (LASSO) is a widely used statistical methodology for simultaneous estimation and variable selection. It is a shrinkage estimation method that allows one to select parsimonious models. In other words, this method estimates the redundant parameters as zero in the large samples and reduces variance of estimates. In recent years, many authors analyzed this technique from a theoretical and applied point of view. We introduce and study the adaptive LASSO problem for discretely observed multivariate diffusion processes. We prove oracle properties and also derive the asymptotic distribution of the LASSO estimator. This is a nontrivial extension of previous results by Wang and Leng (2007, Journal of the American Statistical Association, 102(479), 1039–1048) on LASSO estimation because of different rates of convergence of the estimators in the drift and diffusion coefficients. We perform simulations and real data analysis to provide some evidence on the applicability of this method.

Suggested Citation

  • De Gregorio, Alessandro & Iacus, Stefano M., 2012. "Adaptive Lasso-Type Estimation For Multivariate Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 28(4), pages 838-860, August.
    • Handle: RePEc:cup:etheor:v:28:y:2012:i:04:p:838-860_00
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    Cited by:

    1. Ioane Muni Toke & Nakahiro Yoshida, 2019. "Analyzing order flows in limit order books with ratios of Cox-type intensities," Working Papers hal-01799398, HAL.
    2. Leonid I. Galtchouk & Serge M. Pergamenshchikov, 2022. "Adaptive efficient analysis for big data ergodic diffusion models," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 127-158, April.
    3. Alessandro Gregorio & Francesco Iafrate, 2021. "Regularized bridge-type estimation with multiple penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 921-951, October.
    4. Evgeny Pchelintsev & Serguei Pergamenshchikov & Maria Leshchinskaya, 2022. "Improved estimation method for high dimension semimartingale regression models based on discrete data," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 537-576, October.
    5. De Gregorio, A. & Iacus, S.M., 2013. "On a family of test statistics for discretely observed diffusion processes," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 292-316.
    6. Kou Fujimori, 2019. "The Dantzig selector for a linear model of diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 475-498, October.
    7. A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.
    8. Ioane Muni Toke & Nakahiro Yoshida, 2018. "Analyzing order flows in limit order books with ratios of Cox-type intensities," Papers 1805.06682, arXiv.org, revised Aug 2019.
    9. Ioane Muni Toke & Nakahiro Yoshida, 2020. "Analyzing order flows in limit order books with ratios of Cox-type intensities," Post-Print hal-01799398, HAL.

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