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Konstrukcija meje območja zaupanja : delo diplomskega seminarja
ID Vidic, Luka (Author), ID Smrekar, Jaka (Mentor) More about this mentor... This link opens in a new window

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Abstract
Veliko naprednih statističnih učbenikov predstavi lastnosti asimptotičnih območij zaupanja, vendar večinoma ne predstavijo načinov njihove numerične konstrukcije. V delu diplomskega seminarja je predstavljen koncept računanja meje območja zaupanja in predlog optimizacije. Pri konstrukciji območja zaupanja za izbrani parameter s pomočjo invariantnih testnih statistik lahko uporabimo transformacijo, s pomočjo katere z vsakim izračunom dosežemo mejo območja zaupanja in s tem močno zmanjšamo čas računanja. Koncept je teoretično in praktično zanimiv, saj nam poda metodo, s katero lahko učinkovito konstruiramo območja zaupanja za potrebe primerjanja ali vizualizacije. Predstavimo tudi konkretno implementacijo koncepta v dvorazsežnem primeru za dve različni testni statistiki.

Language:Slovenian
Keywords:invariantnost, numerična optimizacija, reparametrizacija, statistično sklepanje, razmerje verjetij, Hotellingova statistika T^2
Work type:Final seminar paper
Typology:2.11 - Undergraduate Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2021
PID:20.500.12556/RUL-127784 This link opens in a new window
UDC:519.6
COBISS.SI-ID:69463811 This link opens in a new window
Publication date in RUL:23.06.2021
Views:1060
Downloads:115
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Secondary language

Language:English
Title:Construction of the confidence region boundry
Abstract:
Many advanced statistical textbooks present the properties of asymptotic confidence regions, but most do not present methods of their numerical construction. In this work we present the concept of numerical computation of such regions and propose a method for its optimization. When constructing confidence regions for a selected parameter using an invariant test statistic, we may use a simple transformation, which allows us to compute the boundary of the confidence region with each computation and thus greatly reduce computation time. The concept is theoretically and practically interesting, as it gives us a method by which we can effectively construct confidence regions for the purposes of comparison or visualization. We also present a concrete implementation of the concept in the two-dimensional case for two different test statistics.

Keywords:invariance, numerical optimization, reparametrization, statistical inference, likelihood ratio, Hotelling T^2 statistic

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