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Toolbox: Gaussian comparison on Eucledian balls

Author

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  • Koziuk, Andzhey
  • Spokoiny, Vladimir
Abstract
In the work a characterization of difference of multivariate Gaussian measures is found on the family of centered Eucledian balls. In particular, it helps to derive (xx see paper).

Suggested Citation

  • Koziuk, Andzhey & Spokoiny, Vladimir, 2018. "Toolbox: Gaussian comparison on Eucledian balls," IRTG 1792 Discussion Papers 2018-028, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    • Handle: RePEc:zbw:irtgdp:2018028
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    File URL: https://www.econstor.eu/bitstream/10419/230739/1/irtg1792dp2018-028.pdf
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    References listed on IDEAS

    as
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    3. Victor Chernozhukov & Wolfgang K. Hardle & Chen Huang & Weining Wang, 2018. "LASSO-Driven Inference in Time and Space," Papers 1806.05081, arXiv.org, revised May 2020.
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    5. Feng, Zheng-Hui & Lin, Lu & Zhu, Ruo-Qing & Zhu, Li-Xing, 2018. "Nonparametric Variable Selection and Its Application to Additive Models," IRTG 1792 Discussion Papers 2018-002, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    6. Christian M Hafner, 2020. "Testing for Bubbles in Cryptocurrencies with Time-Varying Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 233-249.
    7. Yang, Zihui & Zhou, Yinggang, 2018. "Systemic Risk in Global Volatility Spillover Networks: Evidence from Option-implied Volatility Indices," IRTG 1792 Discussion Papers 2018-003, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
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    9. Efimov, Kirill & Adamyan, Larisa & Spokoiny, Vladimir, 2018. "Adaptive Nonparametric Clustering," IRTG 1792 Discussion Papers 2018-018, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    10. Tryphonides, Andreas, 2018. "Learning from Errors: The case of monetary and fiscal policy regimes," IRTG 1792 Discussion Papers 2018-022, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    11. Chen, Haiqiang & Li, Yingxing & Lin, Ming & Zhu, Yanli, 2018. "A Regime Shift Model with Nonparametric Switching Mechanism," IRTG 1792 Discussion Papers 2018-020, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    12. Härdle, Wolfgang Karl & Chen, Shi & Liang, Chong & Schienle, Melanie, 2018. "Time-varying Limit Order Book Networks," IRTG 1792 Discussion Papers 2018-016, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    13. Almosova, Anna, 2018. "A Monetary Model of Blockchain," IRTG 1792 Discussion Papers 2018-008, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    14. Yi-Hsuan Chen, Cathy & Fengler, Matthias & Härdle, Wolfgang Karl & Liu, Yanchu, 2018. "Textual Sentiment, Option Characteristics, and Stock Return Predictability," Economics Working Paper Series 1808, University of St. Gallen, School of Economics and Political Science.
    15. Davies, Laurie, 2018. "Lasso, knockoff and Gaussian covariates: a comparison," IRTG 1792 Discussion Papers 2018-019, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. Stefan Wagner & Martin C. Goossen, 2018. "Knowing me, knowing you: Inventor mobility and the formation of technology-oriented alliances," ESMT Research Working Papers ESMT-18-01, ESMT European School of Management and Technology.
    17. Götze, Friedrich & Naumov, Alexey & Spokoiny, Vladimir & Ulyanov, Vladimir, 2018. "Large ball probabilities, Gaussian comparison and anti-concentration," IRTG 1792 Discussion Papers 2018-026, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    18. Silin, Igor & Spokoiny, Vladimir, 2018. "Bayesian inference for spectral projectors of covariance matrix," IRTG 1792 Discussion Papers 2018-027, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    19. Lessmann, Stefan & Coussement, Kristof & De Bock, Koen W. & Haupt, Johannes, 2018. "Targeting customers for profit: An ensemble learning framework to support marketing decision making," IRTG 1792 Discussion Papers 2018-012, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    20. Ebert, Johannes & Spokoiny, Vladimir & Suvorikova, Alexandra, 2018. "Construction of Non-asymptotic Confidence Sets in 2 -Wasserstein Space," IRTG 1792 Discussion Papers 2018-025, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    21. Naumov, A. & Spokoiny, V. & Ulyanovk, V., 2018. "Bootstrap Confidence Sets for Spectral Projectors of Sample Covariance," IRTG 1792 Discussion Papers 2018-024, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    22. Almosova, Anna, 2018. "A Monetary Model of Blockchain," VfS Annual Conference 2018 (Freiburg, Breisgau): Digital Economy 181502, Verein für Socialpolitik / German Economic Association.
    23. Hryshchuk, Antanina & Lessmann, Stefan, 2018. "Deregulated day-ahead electricity markets in Southeast Europe: Price forecasting and comparative structural analysis," IRTG 1792 Discussion Papers 2018-009, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    24. Chen, Haiqiang & Li, Yingxing & Lin, Ming & Zhu, Yanli, 2018. "A Regime Shift Model with Nonparametric Switching Mechanism," IRTG 1792 Discussion Papers 2018-048, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
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    Citations

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    Cited by:

    1. Packham, Natalie, 2018. "Optimal contracts under competition when uncertainty from adverse selection and moral hazard are present," IRTG 1792 Discussion Papers 2018-033, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. Qingliang Fan & Wei Zhong, 2018. "Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 388-399, July.
    3. Cai, Zongwu & Fang, Ying & Lin, Ming & Su, Jia, 2018. "Inferences for a Partially Varying Coefficient Model With Endogenous Regressors," IRTG 1792 Discussion Papers 2018-047, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    4. Wang, Honglin & Yu, Fan & Zhou, Yinggang, 2018. "Property Investment and Rental Rate under Housing Price Uncertainty: A Real Options Approach," IRTG 1792 Discussion Papers 2018-051, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    5. Yan, Ji Gao, 2018. "Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables," IRTG 1792 Discussion Papers 2018-040, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    6. Zhong, Wei & Liu, Xi & Ma, Shuangge, 2018. "Variable selection and direction estimation for single-index models via DC-TGDR method," IRTG 1792 Discussion Papers 2018-050, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    7. Guo, Li & Tao, Yubo & Härdle, Wolfgang Karl, 2018. "Understanding Latent Group Structure of Cryptocurrencies Market: A Dynamic Network Perspective," IRTG 1792 Discussion Papers 2018-032, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    8. Kalkbrener, Michael & Packham, Natalie, 2018. "Correlation Under Stress In Normal Variance Mixture Models," IRTG 1792 Discussion Papers 2018-035, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    9. Packham, Natalie & Woebbeking, Fabian, 2018. "A factor-model approach for correlation scenarios and correlation stress-testing," IRTG 1792 Discussion Papers 2018-034, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    10. Chiu, Hsin-Yu & Chiang, Mi-Hsiu & Kuo, Wei-Yu, 2018. "Predicative Ability of Similarity-based Futures Trading Strategies," IRTG 1792 Discussion Papers 2018-045, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    11. Guo, Shaojun & Li, Dong & Li, Muyi, 2018. "Strict Stationarity Testing and GLAD Estimation of Double Autoregressive Models," IRTG 1792 Discussion Papers 2018-049, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    12. Xiaojia Bao & Qingliang Fan, 2020. "The impact of temperature on gaming productivity: evidence from online games," Empirical Economics, Springer, vol. 58(2), pages 835-867, February.
    13. Packham, Natalie & Kalkbrener, Michael & Overbeck, Ludger, 2018. "Default probabilities and default correlations under stress," IRTG 1792 Discussion Papers 2018-037, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    14. Kuczmaszewska, Anna & Yan, Ji Gao, 2018. "On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables," IRTG 1792 Discussion Papers 2018-041, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    15. Chen, Haiqiang & Li, Yingxing & Lin, Ming & Zhu, Yanli, 2018. "A Regime Shift Model with Nonparametric Switching Mechanism," IRTG 1792 Discussion Papers 2018-048, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. Yatracos, Yannis G., 2018. "Residual'S Influence Index (Rinfin), Bad Leverage And Unmasking In High Dimensional L2-Regression," IRTG 1792 Discussion Papers 2018-060, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    17. Zbonakova, Lenka & Li, Xinjue & Härdle, Wolfgang Karl, 2018. "Penalized Adaptive Forecasting with Large Information Sets and Structural Changes," IRTG 1792 Discussion Papers 2018-039, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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    More about this item

    Keywords

    multivariate Gaussian measure; Kolmogorov distance; Gaussian comparison;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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