uu.seUppsala University Publications

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Inference for α-Brownian bridge based on Karhunen-Loève expansionsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); (English)Article in journal (Refereed) Submitted
##### Abstract [en]

##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics
##### Identifiers

URN: urn:nbn:se:uu:diva-232541OAI: oai:DiVA.org:uu-232541DiVA: diva2:748603
#####

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Available from: 2014-09-19 Created: 2014-09-19 Last updated: 2014-10-30
##### In thesis

We study a simple decision problem for the scaling parameter in the α-Brownian bridge X^{(α)} on the interval [0,1]: given two values α_{0}, α_{1} ≥ 0 with α_{0} + α_{1} ≥ 1 and some time 0 ≤ T ≤ 1 we want to test H_{0}: α = α_{0} vs. H_{1}: α = α_{1} based on an observation of X^{(α)} until time T. The likelihood ratio can be written as a functional of a quadratic form ψ(X^{(α)}) of X^{(α)}. In order to calculate the distribution of ψ(X^{(α)}) under the null hypothesis, we generalize the Karhunen-Loève Theorem to positive finite measures on [0,1] and compute the Karhunen-Loève expansion of X^{(α)} under such a measure. Based on this expansion, the distribution of ψ(X^{(α)}) follows by Smirnov's formula.

1. Gaussian Bridges: Modeling and Inference$(function(){PrimeFaces.cw("OverlayPanel","overlay749343",{id:"formSmash:j_idt648:0:j_idt652",widgetVar:"overlay749343",target:"formSmash:j_idt648:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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