2021/04/16 by Fabian Dunker, Dunker, Fabian, Mendoza, Emil +2
Computer Science · Mathematics · #62G05 #62G07 #62P20 #65R30 #65R32 #Applications (stat.AP) #Bayesian Methods and Mixture Models #F.2.1 #FOS: Computer and information sciences #G.1 #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2104.08402
openalex publication_date 2021/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The random coefficients model Yi=β0i+β1i X1i+β2i X2i+…+βdi Xdi, with Xi, Yi, \mathbfβi i.i.d, and \mathbfβi independent of Xi is often used to capture unobserved heterogeneity in a population. We propose a quasi-maximum likelihood method to estimate the joint density distribution of the random coefficient model. This method implicitly involves the inversion of the Radon transformation in order to reconstruct the joint distribution, and hence is an inverse problem. Nonparametric estimation for the joint density of \mathbfβi=(β0i,…, βdi) based on kernel methods or Fourier inversion have been proposed in recent years. Most of these methods assume a heavy tailed design density fX. To add stability to the solution, we apply regularization methods. We analyze the convergence of the method without assuming heavy tails for fX and illustrate performance by applying the method on simulated and real data. To add stability to the solution, we apply a Tikhonov-type regularization method.