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2019 Tests for qualitative features in the random coefficients model
Fabian Dunker, Konstantin Eckle, Katharina Proksch, Johannes Schmidt-Hieber
Electron. J. Statist. 13(2): 2257-2306 (2019). DOI: 10.1214/19-EJS1570


The 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.


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Fabian Dunker. Konstantin Eckle. Katharina Proksch. Johannes Schmidt-Hieber. "Tests for qualitative features in the random coefficients model." Electron. J. Statist. 13 (2) 2257 - 2306, 2019.


Received: 1 July 2018; Published: 2019
First available in Project Euclid: 3 July 2019

zbMATH: 1418.62195
MathSciNet: MR3980958
Digital Object Identifier: 10.1214/19-EJS1570

Primary: 62G10 , 62G15
Secondary: 62G20

Keywords: Gaussian approximation , Ill-posed problems , mode detection , Monotonicity , multiscale statistics , Radon transform , shape constraints


Vol.13 • No. 2 • 2019
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