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[{"key": "dc.contributor.advisor", "value": "Vihola, Matti", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Pohjanheimo, Elviira", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2024-01-30T07:28:00Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2024-01-30T07:28:00Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2023", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/93112", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n tutkielman tarkoituksena on perehty\u00e4 painotusotantaan ja sen varianssin pienent\u00e4miseen vakioivien muuttujien ja sekoitejakaumien avulla. Sek\u00e4 painotusotanta ett\u00e4 vakioivat muuttujat ovat Monte Carlo -menetelmi\u00e4, ja t\u00e4ss\u00e4 tutkielmassa keskityt\u00e4\u00e4n niiden k\u00e4ytt\u00e4miseen odotusarvon integraalin stokastisessa simuloinnissa. Tutkielmassa tarkastellaan kirjallisuudessa esitetty\u00e4 painotusotannan parannusehdotusta, joka mahdollisesti parantaa menetelm\u00e4n tehokkuutta pienent\u00e4m\u00e4ll\u00e4 varianssia ja samalla suojaa menetelm\u00e4\u00e4 ep\u00e4onnistumiselta.\n\nPainotusotanta perustuu todenn\u00e4k\u00f6isyysmitan vaihtamiseen tehokkuuden parantamiseksi. Sen estimaattoriin voidaan lis\u00e4t\u00e4 vakioivat muuttujat, joilla varianssin pienennys perustuu korrelaatioon alkuper\u00e4isen muuttujan ja vakioivan muuttujan v\u00e4lill\u00e4. Vakioivien muuttujien kertoimet t\u00e4ytyy estimoida, sill\u00e4 varianssin pienent\u00e4misen kannalta optimaalisia kertoimia ei yleens\u00e4 voida laskea. T\u00e4m\u00e4n tutkielman p\u00e4\u00e4tuloksena onkin lause, jonka mukaan muutaman ehdon p\u00e4tiess\u00e4 optimaalisten kertoimien korvaaminen pienimm\u00e4n neli\u00f6summan estimaattorilla on vaikutukseltaan asymptoottisesti merkitykset\u00f6nt\u00e4. Sen yksityiskohtaisessa todistuksessa k\u00e4ytet\u00e4\u00e4n todenn\u00e4k\u00f6isyyslaskennan perustuloksia, stokastista kertaluokkaa, matriisilaskentaa sek\u00e4 analyysin differentiaali- ja integraalilaskentaa.\n\nVakioivien muuttujien lis\u00e4ksi painotusotannan parannusehdotukseen liittyy sekoitejakauman k\u00e4ytt\u00e4minen estimaattorissa. Sekoitejakaumalla tarkoitetaan todenn\u00e4k\u00f6isyysjakaumaa, jonka tiheysfunktio on painotettu summa tiheysfunktioista. Yhdist\u00e4m\u00e4ll\u00e4 vakioivat muuttujat ja sekoitejakaumaa k\u00e4ytt\u00e4v\u00e4 painotusotanta saadaan estimaattori, jonka varianssi todistetaan ylh\u00e4\u00e4lt\u00e4 rajoitetuksi. Lis\u00e4ksi osoitetaan, ett\u00e4 menetelm\u00e4n varianssi ei ole suurempi kuin vastaavan painotusotannan varianssi parhaimmillaan. T\u00e4ten, koska estimaattori v\u00e4ltt\u00e4\u00e4 painotusotannan mahdollisen \u00e4\u00e4rett\u00f6m\u00e4n varianssin eik\u00e4 my\u00f6sk\u00e4\u00e4n suurenna varianssia, voidaan todeta, ett\u00e4 parannusehdotusta k\u00e4ytt\u00e4v\u00e4 menetelm\u00e4 on turvallinen ja tehokas versio painotusotannasta.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2024-01-30T07:28:00Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2024-01-30T07:28:00Z (GMT). No. of bitstreams: 0\n Previous issue date: 2023", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "50", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.title", "value": "Painotusotanta vakioivilla muuttujilla ja sekoitejakaumilla", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202401301617", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.copyright", "value": "\u00a9 The Author(s)", "language": null, "element": "rights", "qualifier": "copyright", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "tilastomenetelm\u00e4t", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "Monte Carlo -menetelm\u00e4t", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "simulointi", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matemaattinen tilastotiede", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
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