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    Discrete convolution statistic for hypothesis testing

    Prevedello, Giulio and Duffy, Ken R. (2020) Discrete convolution statistic for hypothesis testing. Communications in Statistics - Theory and Methods. ISSN 1532-415X

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    The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In this case, the computation of classical χ2 statistics, which would not include all observations, results in loss of power, especially when sample sizes are small. Here, as an alternative that uses all data, the maximum likelihood estimator for the distribution of sum of discrete and independent random variables, which we call the convolution statistic, is proposed and its limiting normal covariance matrix determined. To challenge null hypotheses about the distribution of this sum, the generalized Wald’s method is applied to define a testing statistic whose distribution is asymptotic to a χ2 with as many degrees of freedom as the rank of such covariance matrix. Rank analysis also reveals a connection with the roots of the probability generating functions associated to the addend variables of the linear models. A simulation study is performed to compare the convolution test with Pearson’s χ2, and to provide usage guidelines.

    Item Type: Article
    Keywords: iscrete convolution; sum of discrete random variables; statistical hypothesis testing; nonparametric maximum-likelihood estimation; sub-independence;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 15201
    Identification Number:
    Depositing User: Dr Ken Duffy
    Date Deposited: 10 Jan 2022 12:05
    Journal or Publication Title: Communications in Statistics - Theory and Methods
    Publisher: Taylor & Francis
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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