Analysis of Panel Data Under Time-Inhomogeneous Markov Chains

In this slide a new approach for the analysis of panel data is presented. It is based on continuous time-inhomogeneous Markov chains with time-varying covariates dependent transition intensity. Estimation of the regression coefficients of covariates is done using maximum likelihood. Score function and observed information matrix are given explicitly in terms of tensor matrix representations. The information matrix is positive definite regardless the values of statistics of samples paths of Markov chains and the values of covariates. These appealing features allow fast convergence of the coefficient estimates using Newton-Raphson iteration with guaranteed convergence to the true values of parameters. Consistency and large sample properties are established. Numerical study confirms the accuracy of the estimates.