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These studies are available for the following degree students:</p><ul><li>Bachelor's Degree Programme in Mathematics</li><li>Master's Degree Programme in Mathematics</li><li>Bachelor's Degree Programme in Mathematics (Subject Teacher)</li><li>Master's Degree Programme in Mathematics&nbsp;(Subject Teacher)</li><li>Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Doctoral Programme in Mathematics and Statistics</li><li>Doctoral Programme in Mathematics and Science (Specialication in Mathematics)</li><br></ul>","fi":"<p>Tämä opintojakso on tarjolla Matematiikan syventävät opinnot -ristiinopiskeluverkostossa. Verkoston opinnot ovat tarjolla seuraaville opiskelijoille:</p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajien kandidaattiohjelma</li><li>Matematiikan aineenopettajien maisteriohjelma</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan kandidaattiohjelma (matematiikan opintosuunta)</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan maisteriiohjelma (matematiikan opintosuunta)</li><li>Matematiikan ja tilastotieteen tohtoriohjelma</li><li>Matemaattisten tieteiden ja luonnontieteiden tohtoriohjelma (matematiikan opintosuunta)</li><br></ul>"},"cooperationNetwork":{"abbreviation":"matematiikansyventavat","name":{"en":"Cross-institutional studies in advanced courses in mathematics and statistics","fi":"Matematiikan ja tilastotieteen syventävien kurssien ristiinopiskelu","sv":"Korsstudier i fördjupade kurser i matematik och statistik"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"The student acquires knowledge of some basic principles of statitical inference and their theoretical foundations. In particular, the student is able to investigate and describe the asymptotic behaviour of maximum likelihood estimators in large samples, and utilize these results in hypothesis testing and creation of confidence intervals.","fi":"Opiskelija tuntee uskottavuuspohjaisen tilastollisen päättelyn keskeisiä periaatteita ja menetelmien teoreettista perustaa. Erityisesti opiskelija osaa luonnehtia ja tutkia suurimman uskottavuuden estimaattorien asymptoottista käyttäytymistä suurissa otoksissa ja soveltaa näitä tuloksia tilastolliseen testaamiseen sekä luottamusvälien muodostamiseen."},"tweetText":null,"content":{"en":"Sufficient statistics and factorization criterion. Fisher information, score function and information inequality. Delta method. Consistency and asymptotic normality of maximum likelihood estimators. Asymptotic tests.","fi":"Tyhjentävät tunnusluvut ja faktorointikriteeri. Fisherin informaatio, pistemääräfunktio ja informaatioepäyhtälö. Deltamenetelmä. Suurimman uskottavuuden estimaattorien tarkentuvuus ja asymptoottinen normaalisuus. Asymptoottisia tilastollisia testejä."},"additional":{"fi":"Opintojakso on tarjolla joka toinen vuosi ja seuraavan kerran se tarjotaan syksyllä 2026."},"prerequisites":{"en":"Statistical Inference I and II, and their prerequisites.","fi":"Tilastollinen päättely I ja II (TILM3561 ja TILM3562/TILM3707)."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Theory of Statistical Inference","id":"otm-5ba8965d-1481-3799-9ecc-97f42e93ebb7","code":"TILM3519","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-69f8ea31-de0c-3050-ab2a-e571fbab1f95"],"organisations":[],"attainmentLanguages":[],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}