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Linear hypothesis testing for weighted functional data with applications

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  • Łukasz Smaga
  • Jin‐Ting Zhang

Abstract

In socioeconomic areas, functional observations may be collected with weights, called weighted functional data. In this paper, we deal with a general linear hypothesis testing (GLHT) problem in the framework of functional analysis of variance with weighted functional data. With weights taken into account, we obtain unbiased and consistent estimators of the group mean and covariance functions. For the GLHT problem, we obtain a pointwise F‐test statistic and build two global tests, respectively, via integrating the pointwise F‐test statistic or taking its supremum over an interval of interest. The asymptotic distributions of test statistics under the null and some local alternatives are derived. Methods for approximating their null distributions are discussed. An application of the proposed methods to density function data is also presented. Intensive simulation studies and two real data examples show that the proposed tests outperform the existing competitors substantially in terms of size control and power.

Suggested Citation

  • Łukasz Smaga & Jin‐Ting Zhang, 2020. "Linear hypothesis testing for weighted functional data with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 493-515, June.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:2:p:493-515
    DOI: 10.1111/sjos.12414
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    References listed on IDEAS

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