Package: HDElliptical 0.1.3

Long Feng

HDElliptical: High-Dimensional Methods for Elliptically Symmetric Distributions

Fast, documented implementations of robust estimation, testing, dimension reduction, classification, and clustering methods for high-dimensional elliptically symmetric data. Computational kernels use 'Rcpp' and 'RcppArmadillo'. The package follows methods reviewed in Feng (2026), "High-Dimensional Data Analysis for Elliptically Symmetric Distributions" <https://github.com/flnankai/HDElliptical/releases>.

Authors:Long Feng [aut, cre, cph], Dan Zhuang [ctb]

# Install 'HDElliptical' in R:

install.packages('HDElliptical', repos = c('https://flnankai.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/flnankai/hdelliptical/issues

Uses libs:

openblas– Optimized BLAS
c++– GNU Standard C++ Library v3

On CRAN:

openblas cpp

4.60 score 134 downloads 176 exports 3 dependencies

Last updated from:00a73b1ac5. Checks:15 OK. Indexed: yes.

Target	Result	Time
linux-devel-arm64	OK	429
linux-devel-x86_64	OK	530
source / vignettes	OK	729
linux-release-arm64	OK	461
linux-release-x86_64	OK	367
macos-release-arm64	OK	394
macos-release-x86_64	OK	757
macos-oldrel-arm64	OK	371
macos-oldrel-x86_64	OK	879
windows-devel-arm64	OK	762
windows-devel-x86_64	OK	696
windows-release-arm64	OK	882
windows-release-x86_64	OK	651
windows-oldrel-x86_64	OK	691
wasm-release	OK	384

Exports:acg_loglik bai_saranadasa_two_sample_test basic_shape basics_shape bickel_levina_covariance_threshold book_gaussian_alpha_cauchy_test cai_liu_adaptive_covariance_threshold cai_liu_xia_two_sample_test cca_bartlett_test chen_qin_two_sample_test chen_song_feng_rank_white_noise_test chen_zhang_zhong_covariance_test cheng_sscm_equality_test chime_clustering classical_cca classical_cusum_test classical_lda_classifier classical_pca classical_qda_classifier clime_precision composite_t2_two_sample_test conditional_alpha_sieve_design conditional_alpha_sieve_fit conditional_factor_wald_test dsda_classifier ec2_covariance elliptical_factor_number elliptical_factor_precision elliptical_oracle_classifier elliptical_regularized_hotelling_cauchy_test elliptical_regularized_hotelling_test erht_change_point_test erht_wbs fair_classifier fantope_pca feng_jiang_liu_xiong_panel_independence_test feng_lan_liu_ma_alpha_max_test feng_liu_ma_white_noise_test feng_liu_rank_sphericity_test feng_spatial_rank_proportionality_test feng_sun_one_sample_test feng_wang_pdq_two_sample_test feng_zhang_liu_spatial_rank_test feng_zou_wang_two_sample_sign_test feng_zou_wang_zhu_two_sample_test fisher_sun_gallagher_sphericity_test gaussian_alpha_combination_test gaussian_covariance_lrt gaussian_graphical_lasso gaussian_lda_oracle gaussian_mixture_em gaussian_qda_oracle gaussian_wilks_independence_test generalized_sign_pca generic_weighted_hr_location gqda_classifier grs_alpha_test hallin_paindaveine_shape_test hd_classifier_fit high_dimensional_hr hotelling_one_sample_test hotelling_two_sample_test hr_estimator hr_gqda hr_qda if_pca independence_classifier inst_one_sample_test jiang_da_qda john_sphericity_test k_spatial_median kendall_factor_number kendall_pca li_chen_covariance_test li_shao_sparse_qda li_wang_zou_two_sample_sign_test linear_pool_covariance liu_feng_ma_spatial_sign_alpha_test lloyd_kmeans lpd_classifier ma_feng_wang_bao_conditional_alpha_test ma_lan_su_tsai_conditional_alpha_sum_test mauchly_sphericity_test nagao_identity_test normalize_shape ollila_raninen_shrinkage_covariance oracle_weighted_sign_sum_test park_ayyala_one_sample_test pesaran_cd_test pesaran_yamagata_alpha_test pmd_sparse_cca pmd_sparse_pca poet_covariance poet_tme regularized_spatial_sign_covariance relliptical robust_factor_subspace robust_gqda rothman_levina_zhu_covariance_threshold rspherical rts_factor scaled_spatial_median sdar_qda semc_fit semc_select_k_gap shao_threshold_lda sign_whitened_sparse_cca sm_sscm sparse_k_spatial_median sparse_kmeans sparse_kmeans_select_s sparse_kmedian sparse_plugin_lda sparse_plugin_qda sparse_sm_select_k sparse_sm_select_tau sparse_spatial_sign_pca spatial_kendall spatial_median spatial_rank spatial_rank_covariance spatial_rank_test spatial_sign spatial_sign_change_point_test spatial_sign_max_test spatial_sign_maxsum_test spatial_sign_pca spatial_sign_poet spatial_sign_precision spatial_sign_precision_lda spatial_sign_sphericity_test spatial_sign_test spatial_signed_rank_test srivastava_du_one_sample_test srivastava_katayama_kano_two_sample_test sscca sscm sslda ssqda tensor_spatial_sign_precision threshold_spatial_sign_precision threshold_tensor_spatial_sign_precision tinst_two_sample_test truncated_power_pca tyler_shape wang_feng_dms_test wang_liu_feng_ma_serial_panel_test wang_liu_feng_vector_independence_test wang_liu_feng_vector_u_independence_test wang_peng_li_one_sample_test wang_xu_approx_randomization_test wang_yao_corrected_john_test wang_yao_corrected_lrt wang_zhao_feng_wang_mutual_fund_fdr weighted_scaled_spatial_median weighted_spatial_sign_alpha_oracle_test white_noise_portmanteau_test xu_lin_wei_pan_aspu_test yan_zhao_feng_weighted_max_test yan_zhao_feng_weighted_maxsum_test zhang_feng_radial_directional_test zhang_feng_rank_one_sample_test zhang_feng_rank_two_sample_test zhang_zhou_guo_linear_hypothesis_test zhang_zhou_guo_one_sample_test zhang_zhou_guo_paired_test zhang_zhu_zhang_two_sample_test zhao_chen_wang_spatial_sign_white_noise_test zhao_chen_zi_inst_alpha_test zhao_conditional_spatial_sign_sum_test zhao_feng_strongcorr_sign_test zhao_feng_wang_wang_robust_alpha_test zhao_wang_conditional_spatial_sign_test zhao_yang_zhang_feng_wang_adaptive_sphericity_test zhao_yang_zhang_feng_wang_sign_max_test zou_peng_feng_wang_sphericity_test

Dependencies:mvtnorm Rcpp RcppArmadillo

Chapter 1: Robust Directional Foundations

Simulating an elliptical sample | Location and directional covariance | Affine-equivariant shape

Rendered fromchapter-1-foundations.Rmdusingknitr::rmarkdown

Last update: 2026-08-15
Started: 2026-08-15

Chapter 2: Location Tests

Rendered fromchapter-2-location-tests.Rmdusingknitr::rmarkdown

Last update: 2026-08-15
Started: 2026-08-15

Citation

Development and contributors

Readme and manuals

Help Manual

Help page	Topics
Angular central Gaussian log-likelihood	acg_loglik
Original Bai-Saranadasa two-sample mean test	bai_saranadasa_two_sample_test
BASIC bias-adjusted spatial-sign shape estimator	basic_shape
BASICS shrinkage plus bias-adjusted shape estimator	basics_shape
Bickel-Levina hard-thresholded covariance estimator	bickel_levina_covariance_threshold
Book Gaussian alpha Cauchy benchmark	book_gaussian_alpha_cauchy_test
Cai-Liu adaptive covariance thresholding	cai_liu_adaptive_covariance_threshold
Cai-Liu-Xia precision-adjusted two-sample maximum test	cai_liu_xia_two_sample_test
Bartlett likelihood-ratio approximation for canonical correlations	cca_bartlett_test
Chen-Qin two-sample high-dimensional mean test	chen_qin_two_sample_test
Chen-Song-Feng rank-based max white-noise test	chen_song_feng_rank_white_noise_test
Chen-Zhang-Zhong high-dimensional covariance test	chen_zhang_zhong_covariance_test
Cheng-Liu-Peng-Zhang-Zheng two-sample SSCM test	cheng_sscm_equality_test
CHIME clustering for a two-component Gaussian mixture	chime_clustering
Classical canonical correlation analysis	classical_cca
Classical CUSUM change-point test	classical_cusum_test
Classical plug-in linear discriminant classifier	classical_lda_classifier
Classical principal component analysis with explicit covariance convention	classical_pca
Classical plug-in quadratic discriminant classifier	classical_qda_classifier
Classical spatial sign and rank location tests	classical_spatial_tests spatial_rank_test spatial_signed_rank_test spatial_sign_test
Gaussian CLIME sparse precision estimator	clime_precision
Feng-Zou-Wang-Zhu Composite T-squared two-sample test	composite_t2_two_sample_test
Construct a conditional-alpha sieve design from a supplied basis	conditional_alpha_sieve_design
Fit the restricted conditional-alpha sieve regression	conditional_alpha_sieve_fit
Fixed-dimensional conditional-factor Wald benchmark	conditional_factor_wald_test
Direct sparse discriminant analysis	dsda_classifier
EC2 sparse covariance estimation with an eigenvalue constraint	ec2_covariance
Select the number of spikes in an elliptical factor model	elliptical_factor_number
Sparse precision estimation for an elliptical factor fit	elliptical_factor_precision
Exact oracle classifier for two elliptical populations	elliptical_oracle_classifier
Elliptical regularized Hotelling test with Cauchy aggregation	elliptical_regularized_hotelling_cauchy_test
Elliptical regularized Hotelling fixed-ridge test	elliptical_regularized_hotelling_test
Elliptical regularized Hotelling change-point scan	erht_change_point_test
Wild binary segmentation with the ERHT local score	erht_wbs
Features annealed independence rule (FAIR)	fair_classifier
Fantope projection and selection sparse PCA	fantope_pca
Feng-Jiang-Liu-Xiong max-sum panel-independence test	feng_jiang_liu_xiong_panel_independence_test
Feng-Lan-Liu-Ma high-dimensional maximum alpha test	feng_lan_liu_ma_alpha_max_test
Feng-Liu-Ma high-dimensional white-noise test	feng_liu_ma_white_noise_test
Feng-Liu spatial-rank sphericity tests	feng_liu_rank_sphericity_test
Feng-Zhang-Liu spatial-rank proportionality test	feng_spatial_rank_proportionality_test
Feng-Sun scalar-invariant one-sample spatial-sign test	feng_sun_one_sample_test
Feng-Wang pairwise-difference-quantile spatial-sign test	feng_wang_pdq_two_sample_test
Feng-Zhang-Liu high-dimensional two-sample spatial-rank test	feng_zhang_liu_spatial_rank_test
Feng-Zou-Wang two-sample multivariate-sign test	feng_zou_wang_two_sample_sign_test
Feng-Zou-Wang-Zhu scale-invariant Behrens-Fisher test	feng_zou_wang_zhu_two_sample_test
Fisher-Sun-Gallagher fourth-to-second trace sphericity test	fisher_sun_gallagher_sphericity_test
Feng-Lan-Liu-Ma adaptive Gaussian alpha test	gaussian_alpha_combination_test
Classical Gaussian likelihood-ratio test for a covariance matrix	gaussian_covariance_lrt
Gaussian graphical lasso with an off-diagonal penalty	gaussian_graphical_lasso
Oracle Gaussian linear discriminant classifier	gaussian_lda_oracle
Full-covariance Gaussian-mixture EM	gaussian_mixture_em
Oracle Gaussian quadratic discriminant classifier	gaussian_qda_oracle
Gaussian Wilks block-independence test	gaussian_wilks_independence_test
Generalized spatial-sign principal component analysis	generalized_sign_pca
Generic weighted Hettmansperger-Randles location estimator	generic_weighted_hr_location
Generalized quadratic discriminant analysis for elliptical populations	gqda_classifier
Gibbons-Ross-Shanken exact alpha test	grs_alpha_test
Hallin-Paindaveine signed-rank test for elliptical shape	hallin_paindaveine_shape_test
Construct a classifier from a scoring function	hd_classifier_fit
High-dimensional Hettmansperger-Randles estimation	high_dimensional_hr
Classical Hotelling location tests	hotelling_one_sample_test hotelling_tests hotelling_two_sample_test
Hettmansperger-Randles affine-equivariant location and shape	hr_estimator
High-dimensional HR generalized quadratic discriminant analysis	hr_gqda hr_qda
Influential features PCA clustering	if_pca
Diagonal-covariance independence classifier	independence_classifier
Feng-Liu-Ma one-sample inverse norm sign test	inst_one_sample_test
Jiang-Wang-Leng direct sparse QDA	jiang_da_qda
John's classical trace test of Gaussian sphericity	john_sphericity_test
K-spatial-median clustering	k_spatial_median
Robust factor-number selection from multivariate Kendall eigenvalues	kendall_factor_number
Multivariate-Kendall principal component analysis	kendall_pca
Li-Chen two-sample high-dimensional covariance equality test	li_chen_covariance_test
Li-Shao thresholded sparse QDA	li_shao_sparse_qda
Li-Wang-Zou simpler spatial-sign-based two-sample test	li_wang_zou_two_sample_sign_test
Linear or convex pooling of covariance matrices	linear_pool_covariance
Liu-Feng-Ma robust spatial-sign sum alpha test	liu_feng_ma_spatial_sign_alpha_test
Lloyd's deterministic K-means algorithm	lloyd_kmeans
Linear programming discriminant classifier	lpd_classifier
Ma-Feng-Wang-Bao conditional maximum and adaptive alpha test	ma_feng_wang_bao_conditional_alpha_test
Ma-Lan-Su-Tsai conditional high-dimensional alpha sum test	ma_lan_su_tsai_conditional_alpha_sum_test
Mauchly-Box likelihood-ratio test of Gaussian sphericity	mauchly_sphericity_test
Nagao's classical Gaussian identity-covariance test	nagao_identity_test
Normalize a shape matrix	normalize_shape
Ollila-Raninen elliptical shrinkage covariance estimator	ollila_raninen_shrinkage_covariance
Oracle generic weighted-sign sum statistic	oracle_weighted_sign_sum_test
Park-Ayyala one-sample high-dimensional mean test	park_ayyala_one_sample_test
Pesaran CD test for cross-sectional independence	pesaran_cd_test
Pesaran-Yamagata large-N sum alpha test	pesaran_yamagata_alpha_test
Penalized-matrix-decomposition sparse CCA	pmd_sparse_cca
Penalized-matrix-decomposition sparse PCA	pmd_sparse_pca
POET covariance estimator with a supplied factor count	poet_covariance
One-step Tyler POET estimator for an elliptical factor model	poet_tme
Predict from a Chapter 5 classifier	predict.hd_classifier_fit
Predict from a semiparametric elliptical mixture fit	predict.semc_fit
Regularized spatial-sign covariance (RSSCM)	regularized_spatial_sign_covariance
Simulate an elliptically symmetric sample	relliptical
Robust principal subspace for an elliptical factor model	robust_factor_subspace
Generalized QDA from certified robust class fits	robust_gqda
Rothman-Levina-Zhu generalized covariance thresholding	rothman_levina_zhu_covariance_threshold
Simulate a spherically symmetric sample	rspherical
Robust two-step factor estimator based on multivariate Kendall's tau	rts_factor
Scaled spatial median with diagonal HR standardisation	scaled_spatial_median
Sparse discriminant analysis with quadratic interactions	sdar_qda
Semiparametric elliptical mixture clustering	semc_fit
Select the SEMC cluster count by Gap-LSE	semc_select_k_gap
Shao-Wang-Deng-Wang thresholded sparse LDA	shao_threshold_lda
Book sign-whitened sparse CCA variant	sign_whitened_sparse_cca
Spatial-median clustering with a common SSCM metric	sm_sscm
Sparse K-spatial-median clustering	sparse_k_spatial_median
Sparse K-means with ordered-pair BCSS weights	sparse_kmeans
Select the sparse K-means L1 bound by permutation Gap calibration	sparse_kmeans_select_s
Coordinatewise sparse K-median clustering	sparse_kmedian
Sparse matrix plug-in LDA classifier	sparse_plugin_lda
Certified sparse plug-in QDA	sparse_plugin_qda
Select K for Sparse-SM by the BWDM rule	sparse_sm_select_k
Select the Sparse-SM threshold by the permutation Gap criterion	sparse_sm_select_tau
Sparse spatial-sign principal component analysis	sparse_spatial_sign_pca
Multivariate spatial Kendall matrix	spatial_kendall
Spatial median	spatial_median
Empirical spatial ranks	spatial_rank
Spatial rank covariance matrix	spatial_rank_covariance
Spatial signs	spatial_sign
Spatial-sign max-Linf, max-L2, and adaptive change-point test	spatial_sign_change_point_test
Spatial-sign max test for a high-dimensional location	spatial_sign_max_test
Spatial-sign max-sum test for a high-dimensional location	spatial_sign_maxsum_test
Spatial-sign principal component analysis	spatial_sign_pca
Spatial-sign POET estimator for an elliptical factor model	spatial_sign_poet
Robust spatial-sign SCLIME and SGLASSO precision estimation	spatial_sign_precision
Spatial-sign precision plug-in LDA	spatial_sign_precision_lda
Spatial-sign sphericity test	spatial_sign_sphericity_test
Srivastava-Du one-sample high-dimensional mean test	srivastava_du_one_sample_test
Srivastava-Katayama-Kano two-sample mean test	srivastava_katayama_kano_two_sample_test
Primary spatial-sign sparse canonical correlation analysis	sscca
Spatial sign covariance matrix	sscm
Spatial-sign direct sparse linear discriminant analysis	sslda
Spatial-sign sparse quadratic discriminant analysis	ssqda
Sparse tensor-elliptical precision matrices from tensor spatial signs	tensor_spatial_sign_precision
Threshold a spatial-sign precision estimate	threshold_spatial_sign_precision
Threshold fitted tensor spatial-sign precision matrices	threshold_tensor_spatial_sign_precision
Huang-Liu-Zhou-Feng two-sample inverse norm sign test	tinst_two_sample_test
Truncated-power sparse principal components	truncated_power_pca
Tyler's shape estimator	tyler_shape
Wang-Feng double-max-sum change-point test	wang_feng_dms_test
Wang-Liu-Feng-Ma serial-panel Fisher independence test	wang_liu_feng_ma_serial_panel_test
Wang-Liu-Feng rank max-sum test for vector independence	wang_liu_feng_vector_independence_test
Wang-Liu-Feng degenerate rank-U vector-independence test	wang_liu_feng_vector_u_independence_test
Wang-Peng-Li one-sample high-dimensional spatial-sign test	wang_peng_li_one_sample_test
Wang-Xu approximate randomization test	wang_xu_approx_randomization_test
Wang-Yao corrected John's test of sphericity	wang_yao_corrected_john_test
Wang-Yao corrected likelihood-ratio test of sphericity	wang_yao_corrected_lrt
Robust mutual-fund selection with SS-BH or FSS-BH	wang_zhao_feng_wang_mutual_fund_fdr
Weighted scaled spatial median and diagonal HR scale	weighted_scaled_spatial_median
Oracle weighted spatial-sign alpha statistic	weighted_spatial_sign_alpha_oracle_test
Classical Box-Pierce or Ljung-Box white-noise test	white_noise_portmanteau_test
Xu-Lin-Wei-Pan analytical adaptive sum-of-powers test	xu_lin_wei_pan_aspu_test
Yan-Zhao-Feng weighted max test	yan_zhao_feng_weighted_max_test
Yan-Zhao-Feng weighted max-sum test	yan_zhao_feng_weighted_maxsum_test
Zhang-Feng radial-directional test of an elliptical model	zhang_feng_radial_directional_test
Zhang-Feng adaptive marginal-rank location tests	zhang_feng_rank_one_sample_test zhang_feng_rank_tests zhang_feng_rank_two_sample_test
Zhang-Zhou-Guo normal-reference mean tests	zhang_zhou_guo_linear_hypothesis_test zhang_zhou_guo_one_sample_test zhang_zhou_guo_paired_test zhang_zhou_guo_tests
Zhang-Zhu-Zhang normal-reference scale-invariant two-sample test	zhang_zhu_zhang_two_sample_test
Zhao-Chen-Wang spatial-sign white-noise test	zhao_chen_wang_spatial_sign_white_noise_test
Zhao-Chen-Zi inverse-norm sign alpha test	zhao_chen_zi_inst_alpha_test
Zhao robust spatial-sign sum test for conditional alpha	zhao_conditional_spatial_sign_sum_test
Zhao-Feng strong-correlation spatial-sign wild-bootstrap test	zhao_feng_strongcorr_sign_test
Zhao-Feng-Wang-Wang robust maximum and adaptive alpha test	zhao_feng_wang_wang_robust_alpha_test
Zhao-Wang robust conditional maximum and adaptive alpha test	zhao_wang_conditional_spatial_sign_test
Adaptive dense-sparse elliptical sphericity test	zhao_yang_zhang_feng_wang_adaptive_sphericity_test
Zhao-Yang-Zhang-Feng-Wang spatial-sign max sphericity test	zhao_yang_zhang_feng_wang_sign_max_test
Zou-Peng-Feng-Wang spatial-sign sphericity test	zou_peng_feng_wang_sphericity_test