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Testing multivariate hypotheses with positive definite bilinear forms


  • Valentyn Panchenko
  • Cees Diks


In time series analysis, tests for independence, symmetry, and goodness-of-fit based on divergence measures, such as the Kullback-Leibler divergence or Hellinger distance are currently receiving much interest.We consider replacing the divergence measures in these tests by kernel-based positive definite bilinear forms. By doing so, we can use U-statistics estimators for the functional of interest (the divergence between two distributions). In this way we avoid the common practice of using plug-in estimators. In addition, our approach separates the problem of consistent estimation of the divergence measure from that of estimating the underlying joint densities consistently. The approach demonstrates why in a testing context, the bandwidth may tend to zero with the sample size slower than required for consistent density estimation. Our results are illustrated with simulations

Suggested Citation

  • Valentyn Panchenko & Cees Diks, 2004. "Testing multivariate hypotheses with positive definite bilinear forms," Computing in Economics and Finance 2004 201, Society for Computational Economics.
  • Handle: RePEc:sce:scecf4:201

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    More about this item


    Time series; Hypothesis tests; Divergence measures; Bilinear forms;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • 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


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