INTRODUCTION of SELECTED PAPERS

"Bias-Corrected Support Vector Machine with Gaussian Kernel in High-Dimension, Low-Sample-Size Settings"

Working paper


"Quadratic Classifiers for Multiclass High-Dimensional Data"

Working paper


"Principal Component Analysis Based Clustering for High-Dimension, Low-Sample-Size Data"

Working paper

arXiv:
1503.04525
Keywords:
Clustering, Consistency, Geometric representation, HDLSS, Microarray, PC score

"High-Dimensional Quadratic Classifiers in Non-Sparse Settings"

Methodology and Computing in Applied Probability (2018), in press

DOI:
10.1007/s11009-018-9646-z
arXiv:
1503.04549
Keywords:
Asymptotic normality, Bayes error rate, Feature selection, Heterogeneity, Large p small n

"Inference on High-Dimensional Mean Vectors under the Strongly Spiked Eigenvalue Model"

Japanese Journal of Statistics and Data Science, 2 (2019), 105-128.

DOI:
10.1007/s42081-018-0029-z
Keywords:
Asymptotic normality, Data transformation, eigenstructure estimation, Large p small n, Noise reduction methodology, Spiked model

"Distance-Based Classifier by Data Transformation for High-Dimension, Strongly Spiked Eigenvalue Models"

Annals of the Institute of Statistical Mathematics, 71 (2019), 473-503.

DOI:
10.1007/s10463-018-0655-z
arXiv:
1710.10768
Keywords:
Asymptotic normality, Data transformation, Discriminant analysis,
Large p small n, Noise reduction methodology, Spiked model

"Equality Tests of High-Dimensional Covariance Matrices under the Strongly Spiked Eigenvalue Model"

Journal of Statistical Planning and Inference, 202 (2019), 99-111.

DOI:
10.1016/j.jspi.2019.02.002
Keywords:
HDLSS, Large p small n, Noise-reduction methodology, SSE model, Two-sample test

"A Test of Sphericity for High-Dimensional Data and Its Application for Detection of Divergently Spiked Noise"

Sequential Analysis, 37 (2018), 397-411.

DOI:
10.1080/07474946.2018.1548850
Keywords:
Cross-data-matrix method, Gene expression data, HDLSS, Noise detection, Noise-reduction method, Sphericity

"The JSS Award Lecture: High-Dimensional Statistical Analysis: New Developments of Theories and Methodologies"

Journal of the Japan Statistical Society Series J, 48 (2018), 89-111

Keywords:
Data transformation, Discriminant analysis, Geometric representation, HDLSS, Noise-reduction methodology, PCA, Two-sample test

"A Survey of High Dimension Low Sample Size Asymptotics"

Australian & New Zealand Journal of Statistics, Special Issue in Honour of
Peter Gavin Hall, 60 (2018), 4-19

DOI:
10.1111/anzs.12212
Keywords:
Canonical correlations, Classification, Geometric representation, Hypothesis testing, PCA

"Two-Sample Tests for High-Dimension, Strongly Spiked Eigenvalue Models"

Statistica Sinica, 28 (2018), 43-62

arXiv:
1602.02491
DOI:
10.5705/ss.202016.0063
Keywords:
Asymptotic normality, Eigenstructure estimation, Large p small n,
Noise reduction methodology, Spiked model

"Support Vector Machine and Its Bias Correction in High-Dimension, Low-Sample-Size Settings"

Journal of Statistical Planning and Inference, 191 (2017), 88-100

arXiv:
1702.08019
DOI:
10.1016/j.jspi.2017.05.005
Keywords:
Distance-based classifier, HDLSS, Imbalanced data, Large p small n, Multiclass classification

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

American Mathematical Society, Sugaku Expositions, 30 (2017), 137-158

DOI:
10.1090/suga/421

"Non-asymptotic results for Cornish-Fisher expansions"

Journal of Mathematical Sciences, 218 (2016), 363-368

arXiv:
1604.00539
DOI:
10.1007/s10958-016-3036-2
Keywords:
Computable bounds, Non-asymptotic results, Cornish-Fisher expansions

"High-Dimensional Inference on Covariance Structures via the Extended Cross-Data-Matrix Methodology"

Journal of Multivariate Analysis, 151 (2016), 151-166

arXiv:
1503.06492
DOI:
10.1016/j.jmva.2016.07.011
Keywords:
Correlations test, Cross-data-matrix methodology, Graphical modeling, Large p small n, Pathway analysis, RV-coefficient
R-code

"Reconstruction of a High-Dimensional Low-Rank Matrix"

Electronic Journal of Statistics, 10 (2016), 895–917

DOI:
10.1214/16-EJS1128
Keywords:
Eigenstructure, HDLSS, Noise-reduction methodology, PCA, Singular value decomposition

"Asymptotic Properties of the First Principal Component and Equality Tests of Covariance Matrices in High-Dimension, Low-Sample-Size Context"

Journal of Statistical Planning and Inference, 170 (2016), 186-199

arXiv:
1503.07302
DOI:
10.1016/j.jspi.2015.10.007
Keywords:
Contribution ratio, Equality test of covariance matrices, HDLSS, Noise-reduction methodology, PCA

"Geometric Classifier for Multiclass, High-Dimensional Data"

Sequential Analysis, Special Issue: Celebrating Seventy Years of Charles Stein's 1945 Seminal Paper on Two-Stage Sampling, 34 (2015), 279-294

DOI:
10.1080/07474946.2015.1063256
Keywords:
Asymptotic normality, Geometric classifier, HDLSS, Sample size determination, Two-stage procedure

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

Methodology and Computing in Applied Probability, 17 (2015), 419-439

DOI:
10.1007/s11009-013-9370-7
Keywords:
Asymptotic normality, Confidence region, Cross-data-matrix methodology, Large p small n, Microarray, Two-stage procedure

"A Distance-Based, Misclassification Rate Adjusted Classifier for Multiclass, High-Dimensional Data"

Annals of the Institute of Statistical Mathematics, 66 (2014), 983-1010

DOI:
10.1007/s10463-013-0435-8
Keywords:
Asymptotic normality, Distance-based classifier, HDLSS, Sample size determination, Two-stage procedure

"The JSS Research Prize Lecture: Effective Methodologies for High-Dimensional Data"

Journal of the Japan Statistical Society Series J, 43 (2013), 123-150


"PCA Consistency for the Power Spiked Model in High-Dimensional Settings"

Journal of Multivariate Analysis, 122 (2013), 334-354

DOI:
10.1016/j.jmva.2013.08.003
Keywords:
Cross-data-matrix methodology, HDLSS, Large p small n, Microarray data, Noise-reduction methodology


"Correlation Tests for High-Dimensional Data Using Extended Cross-Data-Matrix Methodology"

Journal of Multivariate Analysis, 117 (2013), 313-331

DOI:
10.1016/j.jmva.2013.03.007
Keywords:
Cross-data-matrix methodology, Graphical modeling, HDLSS, High-dimensional regression, Pathway analysis, Two-stage procedure

"Effective PCA for High-Dimension, Low-Sample-Size Data with Noise Reduction via Geometric Representations"

Journal of Multivariate Analysis, 105 (2012), 193-215

DOI:
10.1016/j.jmva.2011.09.002
Keywords:
Consistency, Discriminant analysis, Eigenvalue distribution, Geometric representation, HDLSS, Inverse matrix, Noise reduction, Principal component analysis

"Inference on High-Dimensional Mean Vectors with Fewer Observations Than the Dimension"

Methodology and Computing in Applied Probability, 14 (2012), 459-476

DOI:
10.1007/s11009-011-9233-z
Keywords:
Classification, Confidence region, HDLSS, Sample size determination, Two-stage estimation, Variable selection

"Two-Stage Procedures for High-Dimensional Data"

Sequential Analysis (Editor's special invited paper), 30 (2011), 356-399
[This paper was awarded the Abraham Wald Prize in Sequential Analysis 2012.]

DOI:
10.1080/07474946.2011.619088
Keywords:
Asymptotic normality, Classification, Confidence region, HDLSS, Lasso, Pathway analysis, Regression, Sample size determination, Testing equality of covariance matrices, Two-sample test, Variable selection

"Authors’ Response"

Sequential Analysis, 30 (2011), 432-440

DOI:
10.1080/07474946.2011.619102
Keywords:
Classification, Confidence region, Cross-data-matrix methodology, HDLSS, Robustness, Sample size determination, Two-sample test, Variable selection

"Effective PCA for High-Dimension, Low-Sample-Size Data with Singular Value Decomposition of Cross Data Matrix"

Journal of Multivariate Analysis, 101 (2010), 2060-2077

DOI:
10.1016/j.jmva.2010.04.006
Keywords:
Consistency, Eigenvalue distribution, HDLSS, Microarray data analysis, Mixture model, Principal component analysis, Singular value

"Intrinsic Dimensionality Estimation of High-Dimension, Low Sample Size Data with D-Asymptotics"

Communications in Statistics. Theory and Methods, Special Issue Honoring Akahira, M.
(ed. Aoshima, M.), 39 (2010), 1511-1521

DOI:
10.1080/03610920903121999
Keywords:
Dual covariance matrix, Effective dimension, HDLSS, Large p small n, Maximum eigenvalue

"PCA Consistency for Non-Gaussian Data in High Dimension, Low Sample Size Context"

Communications in Statistics. Theory and Methods, Special Issue Honoring Zacks, S.
(ed. Mukhopadhyay, N.), 38 (2009), 2634-2652

DOI:
10.1080/03610910902936083
Keywords:
Consistency, Dual covariance matrix, Eigenvalue distribution, HDLSS, Large p small n, Principal component analysis, Random matrix theory, Sample size