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dc.contributor.authorHardin, Clyde D., Jren_US
dc.contributor.authorSamorodnitsky, Gennadyen_US
dc.contributor.authorTaqqu, Murad S.en_US
dc.date.accessioned2018-09-05T18:02:13Z
dc.date.available2018-09-05T18:02:13Z
dc.date.issued1991-11
dc.identifierhttps://projecteuclid.org/euclid.aoap/1177005840
dc.identifier.citationClyde D Hardin Jr, Gennady Samorodnitsky, Murad S Taqqu. 1991. "Nonlinear Regression of Stable Random Variables." The Annals of Applied Probability, Volume 1, no. 4. pp. 582 - 612. https://doi.org/10.1214/aoap/1177005840
dc.identifier.urihttps://hdl.handle.net/2144/31174
dc.description.abstractLet (X1,X2) be an α-stable random vector, not necessarily symmetric, with 0<α<2. This article investigates the regression E(X2∣X1=x) for all values of α. We give conditions for the existence of the conditional moment E(|X2|p|X1=x) when p≥α, and we obtain an explicit form of the regression E(X2∣X1=x) as a function of x. Although this regression is, in general, not linear, it can be linear even when the vector (X1,X2) is skewed. We give a necessary and sufficient condition for linearity and characterize the asymptotic behavior of the regression as x→±∞. The behavior of the regression functions is also illustrated graphically.en_US
dc.format.extent582 - 612en_US
dc.languageEN
dc.publisherInstitute of Mathematical Statisticsen_US
dc.relation.ispartofThe Annals of Applied Probability
dc.relation.isversionofhttps://doi.org/10.1214/aoap/1177005840
dc.rights© 1991 Institute of Mathematical Statisticsen_US
dc.subjectApplied mathematicsen_US
dc.subjectStatisticsen_US
dc.subjectStatistics & probabilityen_US
dc.subjectSine functionen_US
dc.subjectMathematical independent variablesen_US
dc.subjectEigenfunctionsen_US
dc.subjectPerceptron convergence procedureen_US
dc.subjectMathematical momentsen_US
dc.subjectNon Gaussianityen_US
dc.titleNonlinear regression of stable random variablesen_US
dc.typeArticleen_US
pubs.elements-sourcemanual-entryen_US
pubs.notesurldate: 2018-05-23 mrnumber: MR1129776 keywords: linear regression, Stable random vectors, symmetric $\textbackslashalpha$-stableen_US
pubs.notesEmbargo: Not knownen_US
pubs.notesArticles older than three years are OA : https://projecteuclid.org/info/euclid.aoapen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
dc.identifier.orcid0000-0002-1145-9082 (Taqqu, Murad S)


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