ﻻ يوجد ملخص باللغة العربية
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.
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We pr
We derive Laplace-approximated maximum likelihood estimators (GLAMLEs) of parameters in our Graph Generalized Linear Latent Variable Models. Then, we study the statistical properties of GLAMLEs when the number of nodes $n_V$ and the observed times of
A maximum likelihood methodology for a general class of models is presented, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC sampler with
CRISPR technology has enabled large-scale cell lineage tracing for complex multicellular organisms by mutating synthetic genomic barcodes during organismal development. However, these sophisticated biological tools currently use ad-hoc and outmoded c
Statistical models with latent structure have a history going back to the 1950s and have seen widespread use in the social sciences and, more recently, in computational biology and in machine learning. Here we study the basic latent class model propo