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Sharp deviation bounds for quadratic forms

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  • Vladimir Spokoiny
  • Mayya Zhilova

Abstract

This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector Xi with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The results are stated under general conditions and do not suppose any special structure of the vector Xi . The obtained bounds are exact (non-asymptotic), all constants are explicit and the leading terms in the bounds are sharp.

Suggested Citation

  • Vladimir Spokoiny & Mayya Zhilova, 2013. "Sharp deviation bounds for quadratic forms," SFB 649 Discussion Papers SFB649DP2013-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2013-035
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2013-035.pdf
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    1. #HEJC papers for September 2013
      by academichealtheconomists in The Academic Health Economists' Blog on 2013-09-01 04:01:38

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    1. Poeschel, Friedrich, 2012. "Assortative matching through signals," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62061, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    quadratic forms; deviation bounds;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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