Regularized maximum likelihood estimation for the random coefficients model
针对随机系数模型，提出一种准最大似然方法来估计系数的联合密度分布，通过Tikhonov正则化解决逆问题的不稳定性，并在无需设计密度重尾假设下分析收敛性，用模拟和真实数据验证效果。
.The random coefficients model Yi=β0i+β1iX1i+β2iX2i+…+βdiXdi, with 𝐗i, Yi, 𝜷i i.i.d, and 𝜷i 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. To add stability to the solution, we apply Tikhonov-type regularization methods. Nonparametric estimation for the joint density of βi=(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. We analyze the convergence of the quasi maximum likelihood method without assuming heavy tails for f𝐗 and illustrate performance by applying the method on simulated and real data.