In this paper, we propose a new methodology to deal with PCA in high-dimension, low-sample-size (HDLSS) data situations. We give an idea of estimating eigenvalues via singular values of a cross data matrix. We provide consistency properties of the eigenvalue estimation as well as its limiting...

In this paper, we propose a general spiked model called the power spiked model in high-dimensional settings. We derive relations among the data dimension, the sample size and the high-dimensional noise structure. We first consider asymptotic properties of the conventional estimator of...

In this paper, we consider tests of correlation when the sample size is much lower than the dimension. We propose a new estimation methodology called the extended cross-data-matrix methodology. By applying the method, we give a new test statistic for high-dimensional correlations. We show that...

In this paper, we consider a scale adjusted-type distance-based classifier for high-dimensional data. We first give such a classifier that can ensure high accuracy in misclassification rates for two-class classification. We show that the classifier is not only consistent but also asymptotically...

A class of discriminant rules which includes Fisher's linear discriminant function and the likelihood ratio criterion is defined. Using asymptotic expansions of the distributions of the discriminant functions in this class, we derive a formula for cut-off points which satisfy some conditions on...

The problem of constructing fixed-width simultaneous confidence intervals for comparing mean vectors ofk([greater-or-equal, slanted]2) independent multivariate normal distributions is considered when those covariance matrices have the intraclass correlation structures. Two-stage procedures are...