{"doi":"10.1109/tit.2021.3088381","title":"Robust Scatter Matrix Estimation for High Dimensional Distributions With Heavy Tail","abstract":"This paper studies large scatter matrix estimation for heavy tailed distributions. The contributions of this paper are twofold. First, we propose and advocate to use a new distribution family, the pair-elliptical, for modeling the high dimensional data. The pair-elliptical is more flexible and easier to check the goodness of fit compared to the elliptical. Secondly, built on the pair-elliptical family, we advocate using quantile-based statistics for estimating the scatter matrix. For this, we provide a family of quantile-based statistics. They outperform the existing ones for better balancing the efficiency and robustness. In particular, we show that the propose estimators have comparable performance to the moment-based counterparts under the Gaussian assumption. The method is also tuning-free compared to Catoni's M-estimator for covariance matrix estimation. We further apply the method to conduct a variety of statistical methods. The corresponding theoretical properties as well as numerical performances are provided.","journal":"IEEE Transactions on Information Theory","year":2021,"id":199007,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":9,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9579,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":414573,"name":"Fang Han","orcid":"0000-0003-2996-5693","position":1,"is_corresponding":false},{"id":774874,"name":"Han Liu","orcid":"0000-0003-0647-6627","position":2,"is_corresponding":false},{"id":311412,"name":"Junwei Lu","orcid":"0000-0003-3743-6855","position":0,"is_corresponding":true}],"reference_count":113,"raw_metadata":null,"created_at":"2026-07-18T23:50:36.595945Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}