Tests for qualitative features in the random coefficients model

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dc.contributor.authorDunker F
dc.contributor.authorEckle K
dc.contributor.authorProksch K
dc.contributor.authorSchmidt-Hieber J
dc.date.accessioned2019-12-02T21:04:38Z
dc.date.available2019-12-02T21:04:38Z
dc.date.issued2019en
dc.date.updated2019-05-15T00:58:13Z
dc.description.abstractThe random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical challenge is to recover information about the joint density of the random coefficients which is a multivariate and ill-posed problem. Because of the curse of dimensionality and the ill-posedness, nonparametric estimation of the joint density is difficult and suffers from slow convergence rates. Larger features, such as an increase of the density along some direction or a well-accentuated mode can, however, be much easier detected from data by means of statistical tests. In this article, we follow this strategy and construct tests and confidence statements for qualitative features of the joint density, such as increases, decreases and modes. We propose a multiple testing approach based on aggregating single tests which are designed to extract shape information on fixed scales and directions. Using recent tools for Gaussian approximations of multivariate empirical processes, we derive expressions for the critical value. We apply our method to simulated and real data.en
dc.identifier.citationDunker F, Eckle K, Proksch K, Schmidt-Hieber J (2019). Tests for qualitative features in the random coefficients model. Electronic Journal of Statistics, Vol. 13 (2019) 2257–2306en
dc.identifier.doihttps://doi.org/10.1214/19-EJS1570
dc.identifier.issn1935-7524
dc.identifier.urihttp://hdl.handle.net/10092/17745
dc.language.isoen
dc.rightsCreative Commons Attribution 4.0 International License.en
dc.subjectGaussian approximationen
dc.subjectmode detectionen
dc.subjectmonotonicityen
dc.subjectmultiscale statisticsen
dc.subjectshape constraintsen
dc.subjectRadon transformen
dc.subjectill-posed problemsen
dc.subject.anzsrcField of Research::01 - Mathematical Sciencesen
dc.titleTests for qualitative features in the random coefficients modelen
dc.typeJournal Articleen
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