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On the density of generalised quadratic forms with applications to asymptotic expansions for test statistics

Author

Listed:
  • Francesco Bravo

Abstract

In this note we derive a general formula useful to express the density of generalised noncentral quadratic forms (i.e. of a scalar random variable obtained by contracting non zero mean multivariate normal vectors over multidimensional arrays) in terms of linear combinations of noncentral chi square random variables. The formula can be used to obtain explicit expressions for the terms appearing in the asymptotic expansions for test statistics under a local alternative.

Suggested Citation

  • Francesco Bravo, "undated". "On the density of generalised quadratic forms with applications to asymptotic expansions for test statistics," Discussion Papers 00/32, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:00/32
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    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2000/0032.pdf
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    More about this item

    Keywords

    Edgeworth expansions; Generalised noncentral quadratic forms; Local alternatives.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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