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Register a new userNonparametric Estimation of the Random Coefficients Model in Python
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Added by
Emil Alfred Edgar Mendoza
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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We present $textbf{PyRMLE}$, a Python module that implements Regularized Maximum Likelihood Estimation for the analysis of Random Coefficient models. $textbf{PyRMLE}$ is simple to use and readily works with data formats that are typical to Random Coefficient problems. The module makes use of Pythons scientific libraries $textbf{NumPy}$ and $textbf{SciPy}$ for computational efficiency. The main implementation of the algorithm is executed purely in Python code which takes advantage of Pythons high-level features.
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The random coefficients model $Y_i={beta_0}_i+{beta_1}_i {X_1}_i+{beta_2}_i {X_2}_i+ldots+{beta_d}_i {X_d}_i$, with $mathbf{X}_i$, $Y_i$, $mathbf{beta}_i$ i.i.d, and $mathbf{beta}_i$ independent of $X_i$ 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 $mathbf{beta}_i=({beta_0}_i,ldots, {beta_d}_i)$ based on kernel methods or Fourier inversion have been proposed in recent years. Most of these methods assume a heavy tailed design density $f_mathbf{X}$. To add stability to the solution, we apply regularization methods. We analyze the convergence of the method without assuming heavy tails for $f_mathbf{X}$ 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.
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