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Inference for General MANOVA Based on ANOVA-Type Statistic

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Advanced Studies in Classification and Data Science

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Abstract

Inference methods for general multivariate analysis of variance (MANOVA) are studied. Homoscedasticity and any particular distribution are not assumed in general factorial designs under consideration. In that general framework, the existing methods based on the Wald-type statistic may behave poorly under finite samples, e.g., they are often too liberal under unbalanced designs and skewed distributions. In this paper, the testing procedures and confidence regions based on the ANOVA-type statistic and its standardized version are proposed, which usually perform very satisfactorily in cases where the known tests fail. Different approaches to approximate the null distribution of test statistics are developed. They are based on asymptotic distribution and bootstrap and permutation methods. The consistency of the asymptotic tests under fixed alternatives is proved. In simulation studies, it is shown that some of the new procedures possess good size and power characteristics, and they are competitive to existing procedures.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland

    Łukasz Smaga

Authors
  1. Łukasz Smaga
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Correspondence to Łukasz Smaga .

Editor information

Editors and Affiliations

  1. School of Management and Information Sciences, Tama University, Tokyo, Japan

    Tadashi Imaizumi

  2. Rikkyo University, Tokyo, Japan

    Akinori Okada

  3. University of Tsukuba, Tsukuba, Japan

    Sadaaki Miyamoto

  4. Department of Mathematics, Chuo University, Tokyo, Japan

    Fumitake Sakaori

  5. Department of Mathematics, Tokai University, Hiratsuka-shi, Japan

    Yoshiro Yamamoto

  6. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Maurizio Vichi

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Smaga, Ł. (2020). Inference for General MANOVA Based on ANOVA-Type Statistic. In: Imaizumi, T., Okada, A., Miyamoto, S., Sakaori, F., Yamamoto, Y., Vichi, M. (eds) Advanced Studies in Classification and Data Science. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Singapore. https://doi.org/10.1007/978-981-15-3311-2_19

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