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Title: Tests for qualitative features in the random coefficients model Authors:  Fabian Dunker - University of Canterbury (New Zealand) [presenting]
Konstantin Eckle - Leiden University (Netherlands)
Katharina Proksch - University of Twente (Netherlands)
Johannes Schmidt-Hieber - University of Twente (Netherlands)
Abstract: The linear random coefficient model $Y_i = \beta_{i,1}X_{i,1} + \beta_{i,2} X_{i,2} + \ldots + \beta_{i,d} X_{i,d}$ is an effective way to model unobserved heterogeneity. Here $(\mathbf{X}_i,Y_i),$ $i=1,\ldots,n,$ are i.i.d. observations with $\mathbf{X}_i=(X_{i,1}, \ldots, X_{i,d})$ being a $d$-dimensional vector of regressors and $Y_i$ a univariate responds. The random coefficients $\boldsymbol{\beta}_i=(\beta_{i,1}, \ldots, \beta_{i,d}),$ $i=1,\ldots,n$ are unobserved i.i.d. realizations of $d$-variate random vector with unknown density $f_{\boldsymbol{\beta}}$ independent of $\mathbf{X}_i$. We propose and analyze a nonparametric multiscale test for slopes and modes of the random coefficient density $f_{\boldsymbol{\beta}}$. The test uses the connection between the model and the d-dimensional Radon transform and is based on Gaussian approximation of empirical processes.