{"doi":"10.1093/biomet/56.2.375","title":"Asymptotic properties of spectral estimates of second order","abstract":null,"journal":"Biometrika","year":1969,"id":630671,"datarank":0.7130385286659547,"base_score":4.7535901911063645,"endowment":4.7535901911063645,"self_citation_contribution":0.7130385286659547,"citation_network_contribution":0.0,"self_endowment_contribution":0.7130385286659547,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":115,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1633926,"name":"DAVID R. BRILLINGER","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Asymptotic properties of spectral estimates of second order","abstract":"Let X(t) (t = 0, ± 1,…) be a zero mean, r vector-valued, strictly stationary time series satisfying a particular assumption about the near-independence of widely separated values. Given the values X(t) (t = 0, 1,…, T− 1), we construct the statistics: I(T)/XX(γ)(-∞λlt;∞),the matrix of second-order periodograms, FT/XX(λ),the matrix of sample spectral measures, fT/XX(λ), the matrix of sample spectral densities and c(T)/(u) (u = 0,± 1,…), the matrix of sample covariances. In the paper expressions are derived for the first- and second-order moments and the asymptotic distributions of IT/XX(λ), F(T)/XX(λ), f(T)/XX(λ) and c(T)/XX(u). Our purpose is to determine the form of these moments and to indicate the appearance of the Wishart distribution as an exact limiting distribution for f(T)/XX(λ). It has previously been suggested as an approximation.","is_dataset_classified":null,"base_score":4.7535901911063645,"endowment":4.7535901911063645,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"19767382","pmcid":null,"openalex_id":"https://openalex.org/W2069698042","authors":[],"funders":[],"total_grants":0,"fwci":6.0028,"citation_percentile":0.96046512,"influential_citations":0,"citation_trend":[{"year":2012,"count":2},{"year":2013,"count":1},{"year":2014,"count":2},{"year":2016,"count":3},{"year":2017,"count":3},{"year":2018,"count":1},{"year":2019,"count":2},{"year":2020,"count":2},{"year":2021,"count":2},{"year":2022,"count":1},{"year":2023,"count":2},{"year":2024,"count":1},{"year":2025,"count":1},{"year":2026,"count":1}],"oa_status":"closed","license":null,"oa_locations":[{"url":"http://academic.oup.com/biomet/article-pdf/56/2/375/583022/56-2-375.pdf","host_type":"publisher"},{"url":"https://doi.org/10.1093/biomet/56.2.375","host_type":"journal"}],"fields_of_study":["Blind Source Separation Techniques","Statistical and numerical algorithms","Matrix Theory and Algorithms"],"mesh_terms":[],"keywords":["Mathematics","Wishart distribution","Series (stratigraphy)","Matrix (chemical analysis)","Combinatorics","Order (exchange)","Zero (linguistics)","Distribution (mathematics)","Asymptotic expansion","Statistics","Mathematical analysis","Multivariate statistics"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-05T21:53:38.738867Z","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":[]}