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Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable one-dimensional (1D) algorithm for estimating an envelope in general. We reveal an important structural property of envelopes that facilitates our algorithm, and we prove both Fisher consistency and n-consistency of the algorithm.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0iVVRGLTgiPz4KPHJlc291cmNlIHhtbG5zPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCIgeG1sbnM6eHNpPSJodHRwOi8vd3d3LnczLm9yZy8yMDAxL1hNTFNjaGVtYS1pbnN0YW5jZSIgeHNpOnNjaGVtYUxvY2F0aW9uPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCBodHRwOi8vc2NoZW1hLmRhdGFjaXRlLm9yZy9tZXRhL2tlcm5lbC00LjQvbWV0YWRhdGEueHNkIj4KICA8aWRlbnRpZmllciBpZGVudGlmaWVyVHlwZT0iRE9JIj4xMC42MDg0L005LkZJR1NIQVJFLkMuMjA1ODE0NjwvaWRlbnRpZmllcj4KICA8Y3JlYXRvcnM+CiAgICA8Y3JlYXRvcj4KICAgICAgPGNyZWF0b3JOYW1lPlIuIERlbm5pcyBDb29rPC9jcmVhdG9yTmFtZT4KICAgICAgPGdpdmVuTmFtZT5SLjwvZ2l2ZW5OYW1lPgogICAgICA8ZmFtaWx5TmFtZT5EZW5uaXMgQ29vazwvZmFtaWx5TmFtZT4KICAgIDwvY3JlYXRvcj4KICAgIDxjcmVhdG9yPgogICAgICA8Y3JlYXRvck5hbWU+WGluIFpoYW5nPC9jcmVhdG9yTmFtZT4KICAgICAgPGdpdmVuTmFtZT5YaW48L2dpdmVuTmFtZT4KICAgICAgPGZhbWlseU5hbWU+Wmhhbmc8L2ZhbWlseU5hbWU+CiAgICA8L2NyZWF0b3I+CiAgPC9jcmVhdG9ycz4KICA8dGl0bGVzPgogICAgPHRpdGxlPkFsZ29yaXRobXMgZm9yIEVudmVsb3BlIEVzdGltYXRpb248L3RpdGxlPgogIDwvdGl0bGVzPgogIDxkZXNjcmlwdGlvbnM+CiAgICA8ZGVzY3JpcHRpb24gZGVzY3JpcHRpb25UeXBlPSJBYnN0cmFjdCI+Jmx0O2RpdiZndDsmbHQ7cCZndDsmbHQ7L3AmZ3Q7Jmx0O3AmZ3Q7RW52ZWxvcGVzIHdlcmUgcmVjZW50bHkgcHJvcG9zZWQgYXMgbWV0aG9kcyBmb3IgcmVkdWNpbmcgZXN0aW1hdGl2ZSB2YXJpYXRpb24gaW4gbXVsdGl2YXJpYXRlIGxpbmVhciByZWdyZXNzaW9uLiBFc3RpbWF0aW9uIG9mIGFuIGVudmVsb3BlIHVzdWFsbHkgaW52b2x2ZXMgb3B0aW1pemF0aW9uIG92ZXIgR3Jhc3NtYW5uIG1hbmlmb2xkcy4gV2UgcHJvcG9zZSBhIGZhc3QgYW5kIHdpZGVseSBhcHBsaWNhYmxlIG9uZS1kaW1lbnNpb25hbCAoMUQpIGFsZ29yaXRobSBmb3IgZXN0aW1hdGluZyBhbiBlbnZlbG9wZSBpbiBnZW5lcmFsLiBXZSByZXZlYWwgYW4gaW1wb3J0YW50IHN0cnVjdHVyYWwgcHJvcGVydHkgb2YgZW52ZWxvcGVzIHRoYXQgZmFjaWxpdGF0ZXMgb3VyIGFsZ29yaXRobSwgYW5kIHdlIHByb3ZlIGJvdGggRmlzaGVyIGNvbnNpc3RlbmN5IGFuZCAmbHQ7L3AmZ3Q7Jmx0O3AmZ3Q7Jmx0Oy9wJmd0OyZsdDtwJmd0OyZsdDsvcCZndDsmbHQ7cCZndDsmbHQ7bWkmZ3Q7biZsdDsvbWkmZ3Q7Jmx0Oy9wJmd0OyZsdDtwJmd0OyZsdDsvcCZndDsmbHQ7cCZndDsmbHQ7L3AmZ3Q7LWNvbnNpc3RlbmN5IG9mIHRoZSBhbGdvcml0aG0uJmx0O3AmZ3Q7Jmx0Oy9wJmd0OyZsdDsvZGl2Jmd0OzwvZGVzY3JpcHRpb24+CiAgPC9kZXNjcmlwdGlvbnM+CiAgPHN1YmplY3RzPgogICAgPHN1YmplY3Q+Vmlyb2xvZ3k8L3N1YmplY3Q+CiAgICA8c3ViamVjdD5JbmZlY3Rpb3VzIERpc2Vhc2VzPC9zdWJqZWN0PgogICAgPHN1YmplY3Q+TWF0aGVtYXRpY3M8L3N1YmplY3Q+CiAgICA8c3ViamVjdD5JbmZvcm1hdGlvbiBhbmQgQ29tcHV0aW5nIFNjaWVuY2VzPC9zdWJqZWN0PgogICAgPHN1YmplY3Q+QmlvbG9naWNhbCBTY2llbmNlczwvc3ViamVjdD4KICAgIDxzdWJqZWN0PkVjb2xvZ3k8L3N1YmplY3Q+CiAgICA8c3ViamVjdD5FYXJ0aCBhbmQgRW52aXJvbm1lbnRhbCBTY2llbmNlczwvc3ViamVjdD4KICAgIDxzdWJqZWN0PkNlbGwgQmlvbG9neTwvc3ViamVjdD4KICAgIDxzdWJqZWN0Pk1lZGljaW5lPC9zdWJqZWN0PgogICAgPHN1YmplY3Q+RW5naW5lZXJpbmc8L3N1YmplY3Q+CiAgPC9zdWJqZWN0cz4KICA8cHVibGlzaGVyPlRheWxvciAmYW1wOyBGcmFuY2lzPC9wdWJsaXNoZXI+CiAgPHB1YmxpY2F0aW9uWWVhcj4yMDE1PC9wdWJsaWNhdGlvblllYXI+CiAgPGRhdGVzPgogICAgPGRhdGUgZGF0ZVR5cGU9IkNyZWF0ZWQiPjIwMTUtMTItMDU8L2RhdGU+CiAgICA8ZGF0ZSBkYXRlVHlwZT0iVXBkYXRlZCI+MjAxOS0wOC0xOTwvZGF0ZT4KICA8L2RhdGVzPgogIDxyZXNvdXJjZVR5cGUgcmVzb3VyY2VUeXBlR2VuZXJhbD0iQ29sbGVjdGlvbiI+Q29sbGVjdGlvbjwvcmVzb3VyY2VUeXBlPgogIDxyaWdodHNMaXN0PgogICAgPHJpZ2h0cyByaWdodHNVUkk9Imh0dHBzOi8vY3JlYXRpdmVjb21tb25zLm9yZy9saWNlbnNlcy9ieS80LjAvIj5DQyBCWSA0LjA8L3JpZ2h0cz4KICA8L3JpZ2h0c0xpc3Q+CjwvcmVzb3VyY2U+","url":"https://tandf.figshare.com/collections/Algorithms_for_Envelope_Estimation/2058146","contentUrl":null,"metadataVersion":2,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2015-12-05T17:37:01.000Z","registered":"2015-12-05T17:37:03.000Z","published":"2015","updated":"2024-03-21T08:41:47.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.c.2058146","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}