B1098
Title: Multiscale tests for shape constraints in linear random coefficient models
Authors: Fabian Dunker - University of Canterbury (New Zealand) [presenting]
Konstantin Eckle - Ruhr-Universitaet Bochum (Germany)
Katharina Proksch - University of Goettingen (Germany)
Johannes Schmidt-Hieber - Leiden University (Netherlands)
Abstract: A popular way to model unobserved heterogeneity is the linear random coefficient models $Y_i = \beta_{i,1}X_{i,1} + \beta_{i,2} X_{i,2} + \ldots + \beta_{i,d} X_{i,d}$. We assume that the observations $(\mathbf{X}_i,Y_i)$, $i=1,\ldots,n,$, are i.i.d. where $\mathbf{X}_i=(X_{i,1}, \ldots, X_{i,d})$ is a $d$-dimensional vector of regressors. The random coefficients $\boldsymbol{\beta}_i=(\beta_{i,1}, \ldots, \beta_{i,d})$, $i=1,\ldots,n$ are unobserved i.i.d. realizations of an unknown $d$-dimensional distribution with density $f_{\boldsymbol{\beta}}$ independent of $\mathbf{X}_i$. We propose and analyze a nonparametric multiscale test for shape constraints of the random coefficient density $f_{\boldsymbol{\beta}}$. In particular we are interested in confidence sets for slopes and modes of the density. The test uses the connection between the model and the $d$-dimensional Radon transform and is based on Gaussian approximation of empirical processes.
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