Authors' Response

Methodol Comput Appl Probab

2013

Self Cite

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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Section: Confidence Region Formentioning

confidence: 99%

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

Methodol Comput Appl Probab

2013

Self Cite

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“…Aoshima and Yata [2,3] developed a variety of high-dimensional statistical inference based on the geometric representations such as given-bandwidth confidence region, two-sample test, classification, variable selection, regression, pathway analysis and so on. They provided sample size determination to ensure prespecified high accuracy for each inference even when the population distribution is non-Gaussian.…”

Section: Introductionmentioning

confidence: 99%

Statistical inference for high-dimension, low-sample-size data

2017

Sugaku Expositions

In this paper, we consider statistical inference for high-dimension, low-sample-size (HDLSS) data. We first show that HDLSS data have distinct geometric representations depending on whether or not the data meets a certain boundary condition. We clarify the limit of the conventional principal component analysis (PCA) for HDLSS data. In order to overcome the curse of dimensionality, we introduce two effective PCAs called the noisereduction methodology and the cross-data-matrix (CDM) methodology. We further introduce the extended CDM methodology, which offers an unbiased estimator having small asymptotic variance and low computational cost, for feature parameters appearing in high-dimensional data analysis. We give correlation tests and several inferences on multiclass mean vectors for HDLSS data, and discuss sample size determination to ensure prespecified high accuracy for inference. Finally, we introduce two effective discriminant procedures: the geometric classifier and the distance-based classifier, that can hold misclassification rates less than a threshold. This article originally appeared in Japanese in Sūgaku 65 (3) (2013), 225-247.

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A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data

2013

Ann Inst Stat Math