{"data":{"id":"10.6084/m9.figshare.1568438","type":"dois","attributes":{"doi":"10.6084/m9.figshare.1568438","prefix":"10.6084","suffix":"m9.figshare.1568438","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Ziqi Chen","affiliation":[],"nameIdentifiers":[]},{"name":"Chenlei Leng","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Dynamic Covariance Models"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2016,"subjects":[{"subject":"Genetics"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Ecology"},{"subject":"Sociology"},{"subject":"FOS: Sociology","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Sociology","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"69999 Biological Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"80699 Information Systems not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Computer and information sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Computer and information sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"19999 Mathematical Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"}],"contributors":[],"dates":[{"date":"2015-10-08","dateType":"Created"},{"date":"2018-06-06","dateType":"Updated"},{"date":"2016","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/01621459.2015.1077712","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["387295 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"An important problem in contemporary statistics is to understand the relationship among a large number of variables based on a dataset, usually with \u003ci\u003ep\u003c/i\u003e, the number of the variables, much larger than \u003ci\u003en\u003c/i\u003e, the sample size. Recent efforts have focused on modeling static covariance matrices where pairwise covariances are considered invariant. In many real systems, however, these pairwise relations often change. To characterize the changing correlations in a high-dimensional system, we study a class of dynamic covariance models (DCMs) assumed to be sparse, and investigate for the first time a unified theory for understanding their nonasymptotic error rates and model selection properties. In particular, in the challenging high-dimensional regime, we highlight a new uniform consistency theory in which the sample size can be seen as \u003ci\u003en\u003c/i\u003e\u003csup\u003e4/5\u003c/sup\u003e when the bandwidth parameter is chosen as \u003ci\u003eh\u003c/i\u003e∝\u003ci\u003en\u003c/i\u003e\u003csup\u003e− 1/5\u003c/sup\u003e for accounting for the dynamics. We show that this result holds uniformly over a range of the variable used for modeling the dynamics. The convergence rate bears the mark of the familiar bias-variance trade-off in the kernel smoothing literature. We illustrate the results with simulations and the analysis of a neuroimaging dataset. Supplementary materials for this article are available online.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0iVVRGLTgiPz4KPHJlc291cmNlIHhtbG5zPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCIgeG1sbnM6eHNpPSJodHRwOi8vd3d3LnczLm9yZy8yMDAxL1hNTFNjaGVtYS1pbnN0YW5jZSIgeHNpOnNjaGVtYUxvY2F0aW9uPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCBodHRwOi8vc2NoZW1hLmRhdGFjaXRlLm9yZy9tZXRhL2tlcm5lbC00LjEvbWV0YWRhdGEueHNkIj4KICA8aWRlbnRpZmllciBpZGVudGlmaWVyVHlwZT0iRE9JIj4xMC42MDg0L005LkZJR1NIQVJFLjE1Njg0Mzg8L2lkZW50aWZpZXI+CiAgPGNyZWF0b3JzPgogICAgPGNyZWF0b3I+CiAgICAgIDxjcmVhdG9yTmFtZT5aaXFpIENoZW48L2NyZWF0b3JOYW1lPgogICAgPC9jcmVhdG9yPgogICAgPGNyZWF0b3I+CiAgICAgIDxjcmVhdG9yTmFtZT5DaGVubGVpIExlbmc8L2NyZWF0b3JOYW1lPgogICAgPC9jcmVhdG9yPgogIDwvY3JlYXRvcnM+CiAgPHRpdGxlcz4KICAgIDx0aXRsZT5EeW5hbWljIENvdmFyaWFuY2UgTW9kZWxzPC90aXRsZT4KICA8L3RpdGxlcz4KICA8ZGVzY3JpcHRpb25zPgogICAgPGRlc2NyaXB0aW9uIGRlc2NyaXB0aW9uVHlwZT0iQWJzdHJhY3QiPiZsdDtwJmd0O0FuIGltcG9ydGFudCBwcm9ibGVtIGluIGNvbnRlbXBvcmFyeSBzdGF0aXN0aWNzIGlzIHRvIHVuZGVyc3RhbmQgdGhlIHJlbGF0aW9uc2hpcCBhbW9uZyBhIGxhcmdlIG51bWJlciBvZiB2YXJpYWJsZXMgYmFzZWQgb24gYSBkYXRhc2V0LCB1c3VhbGx5IHdpdGggJmx0O2kmZ3Q7cCZsdDsvaSZndDssIHRoZSBudW1iZXIgb2YgdGhlIHZhcmlhYmxlcywgbXVjaCBsYXJnZXIgdGhhbiAmbHQ7aSZndDtuJmx0Oy9pJmd0OywgdGhlIHNhbXBsZSBzaXplLiBSZWNlbnQgZWZmb3J0cyBoYXZlIGZvY3VzZWQgb24gbW9kZWxpbmcgc3RhdGljIGNvdmFyaWFuY2UgbWF0cmljZXMgd2hlcmUgcGFpcndpc2UgY292YXJpYW5jZXMgYXJlIGNvbnNpZGVyZWQgaW52YXJpYW50LiBJbiBtYW55IHJlYWwgc3lzdGVtcywgaG93ZXZlciwgdGhlc2UgcGFpcndpc2UgcmVsYXRpb25zIG9mdGVuIGNoYW5nZS4gVG8gY2hhcmFjdGVyaXplIHRoZSBjaGFuZ2luZyBjb3JyZWxhdGlvbnMgaW4gYSBoaWdoLWRpbWVuc2lvbmFsIHN5c3RlbSwgd2Ugc3R1ZHkgYSBjbGFzcyBvZiBkeW5hbWljIGNvdmFyaWFuY2UgbW9kZWxzIChEQ01zKSBhc3N1bWVkIHRvIGJlIHNwYXJzZSwgYW5kIGludmVzdGlnYXRlIGZvciB0aGUgZmlyc3QgdGltZSBhIHVuaWZpZWQgdGhlb3J5IGZvciB1bmRlcnN0YW5kaW5nIHRoZWlyIG5vbmFzeW1wdG90aWMgZXJyb3IgcmF0ZXMgYW5kIG1vZGVsIHNlbGVjdGlvbiBwcm9wZXJ0aWVzLiBJbiBwYXJ0aWN1bGFyLCBpbiB0aGUgY2hhbGxlbmdpbmcgaGlnaC1kaW1lbnNpb25hbCByZWdpbWUsIHdlIGhpZ2hsaWdodCBhIG5ldyB1bmlmb3JtIGNvbnNpc3RlbmN5IHRoZW9yeSBpbiB3aGljaCB0aGUgc2FtcGxlIHNpemUgY2FuIGJlIHNlZW4gYXMgJmx0O2kmZ3Q7biZsdDsvaSZndDsmbHQ7c3VwJmd0OzQvNSZsdDsvc3VwJmd0OyB3aGVuIHRoZSBiYW5kd2lkdGggcGFyYW1ldGVyIGlzIGNob3NlbiBhcyAmbHQ7aSZndDtoJmx0Oy9pJmd0O+KInSZsdDtpJmd0O24mbHQ7L2kmZ3Q7Jmx0O3N1cCZndDviiJIgMS81Jmx0Oy9zdXAmZ3Q7IGZvciBhY2NvdW50aW5nIGZvciB0aGUgZHluYW1pY3MuIFdlIHNob3cgdGhhdCB0aGlzIHJlc3VsdCBob2xkcyB1bmlmb3JtbHkgb3ZlciBhIHJhbmdlIG9mIHRoZSB2YXJpYWJsZSB1c2VkIGZvciBtb2RlbGluZyB0aGUgZHluYW1pY3MuIFRoZSBjb252ZXJnZW5jZSByYXRlIGJlYXJzIHRoZSBtYXJrIG9mIHRoZSBmYW1pbGlhciBiaWFzLXZhcmlhbmNlIHRyYWRlLW9mZiBpbiB0aGUga2VybmVsIHNtb290aGluZyBsaXRlcmF0dXJlLiBXZSBpbGx1c3RyYXRlIHRoZSByZXN1bHRzIHdpdGggc2ltdWxhdGlvbnMgYW5kIHRoZSBhbmFseXNpcyBvZiBhIG5ldXJvaW1hZ2luZyBkYXRhc2V0LiBTdXBwbGVtZW50YXJ5IG1hdGVyaWFscyBmb3IgdGhpcyBhcnRpY2xlIGFyZSBhdmFpbGFibGUgb25saW5lLiZsdDsvcCZndDs8L2Rlc2NyaXB0aW9uPgogIDwvZGVzY3JpcHRpb25zPgogIDxzdWJqZWN0cz4KICAgIDxzdWJqZWN0PkdlbmV0aWNzPC9zdWJqZWN0PgogICAgPHN1YmplY3Q+RWNvbG9neTwvc3ViamVjdD4KICAgIDxzdWJqZWN0PlNvY2lvbG9neTwvc3ViamVjdD4KICAgIDxzdWJqZWN0IHNjaGVtZVVSST0iaHR0cDovL3d3dy5hYnMuZ292LmF1L2F1c3N0YXRzL2Fic0AubnNmLzAvNkJCNDI3QUI5Njk2QzIyNUNBMjU3NDE4MDAwNDQ2M0UiIHN1YmplY3RTY2hlbWU9IkZPUiI+Njk5OTkgQmlvbG9naWNhbCBTY2llbmNlcyBub3QgZWxzZXdoZXJlIGNsYXNzaWZpZWQ8L3N1YmplY3Q+CiAgICA8c3ViamVjdCBzY2hlbWVVUkk9Imh0dHA6Ly93d3cuYWJzLmdvdi5hdS9hdXNzdGF0cy9hYnNALm5zZi8wLzZCQjQyN0FCOTY5NkMyMjVDQTI1NzQxODAwMDQ0NjNFIiBzdWJqZWN0U2NoZW1lPSJGT1IiPjgwNjk5IEluZm9ybWF0aW9uIFN5c3RlbXMgbm90IGVsc2V3aGVyZSBjbGFzc2lmaWVkPC9zdWJqZWN0PgogICAgPHN1YmplY3Qgc2NoZW1lVVJJPSJodHRwOi8vd3d3LmFicy5nb3YuYXUvYXVzc3RhdHMvYWJzQC5uc2YvMC82QkI0MjdBQjk2OTZDMjI1Q0EyNTc0MTgwMDA0NDYzRSIgc3ViamVjdFNjaGVtZT0iRk9SIj4xOTk5OSBNYXRoZW1hdGljYWwgU2NpZW5jZXMgbm90IGVsc2V3aGVyZSBjbGFzc2lmaWVkPC9zdWJqZWN0PgogIDwvc3ViamVjdHM+CiAgPHB1Ymxpc2hlcj5UYXlsb3IgJmFtcDsgRnJhbmNpczwvcHVibGlzaGVyPgogIDxwdWJsaWNhdGlvblllYXI+MjAxNjwvcHVibGljYXRpb25ZZWFyPgogIDxkYXRlcz4KICAgIDxkYXRlIGRhdGVUeXBlPSJDcmVhdGVkIj4yMDE1LTEwLTA4PC9kYXRlPgogICAgPGRhdGUgZGF0ZVR5cGU9IlVwZGF0ZWQiPjIwMTgtMDYtMDY8L2RhdGU+CiAgPC9kYXRlcz4KICA8cmVzb3VyY2VUeXBlIHJlc291cmNlVHlwZUdlbmVyYWw9IkRhdGFzZXQiPkRhdGFzZXQ8L3Jlc291cmNlVHlwZT4KICA8c2l6ZXM+CiAgICA8c2l6ZT4zODcyOTUgQnl0ZXM8L3NpemU+CiAgPC9zaXplcz4KICA8cmVsYXRlZElkZW50aWZpZXJzPgogICAgPHJlbGF0ZWRJZGVudGlmaWVyIHJlbGF0ZWRJZGVudGlmaWVyVHlwZT0iRE9JIiByZWxhdGlvblR5cGU9IklzU3VwcGxlbWVudFRvIj4xMC4xMDgwLzAxNjIxNDU5LjIwMTUuMTA3NzcxMjwvcmVsYXRlZElkZW50aWZpZXI+CiAgPC9yZWxhdGVkSWRlbnRpZmllcnM+CiAgPHJpZ2h0c0xpc3Q+CiAgICA8cmlnaHRzIHJpZ2h0c1VSST0iaHR0cHM6Ly9jcmVhdGl2ZWNvbW1vbnMub3JnL2xpY2Vuc2VzL2J5LzQuMC8iPkNDIEJZIDQuMDwvcmlnaHRzPgogIDwvcmlnaHRzTGlzdD4KPC9yZXNvdXJjZT4=","url":"https://tandf.figshare.com/articles/dataset/Dynamic_Covariance_Models/1568438","contentUrl":null,"metadataVersion":6,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCo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