Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions

Abstract

In this paper, we consider the asymptotic normality for various inference problems on multisample and high-dimensional mean vectors. We verify that the asymptotic normality of concerned statistics is proved under mild conditions for high-dimensional data. We show that the asymptotic normality can be justified theoretically and numerically even for non-Gaussian data. We introduce the extended cross-data-matrix (ECDM) methodology to construct an unbiased estimator at a reasonable computational cost. With the help of the asymptotic normality, we show that the concerned statistics given by ECDM can ensure consistency properties for inference on multisample and high-dimensional mean vectors. We give several applications such as confidence regions for high-dimensional mean vectors, confidence intervals for the squared norm and the test of multisample mean vectors. We also provide sample size determination so as to satisfy prespecified accuracy on inference. Finally, we give several examples by using a microarray data set.

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Correspondence to Makoto Aoshima.

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Aoshima, M., Yata, K. Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions. Methodol Comput Appl Probab 17, 419–439 (2015). https://doi.org/10.1007/s11009-013-9370-7

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Keywords

  • Asymptotic normality
  • Confidence region
  • Cross-data-matrix methodology
  • Large p small n
  • Microarray
  • Two-stage procedure

AMS 2000 Subject Classifications

  • 62H10
  • 62L10
  • 60F05