Kernel mode-based varying coefficient models with nonstationary regressors

We propose estimating varying coefficient models based on the mode value using a kernel objective function, allowing for both stationary and unit root regressors. This kernel mode-based estimation is more robust and efficient than least squares estimation for data with outliers or heavy-tailed distributions, without sacrificing efficiency when the data follow a normal distribution. We develop a local linear approximation scheme to estimate the varying coefficient function. We show that the nonparametric estimator of the varying coefficient function with nonstationary regressors converges faster than the estimator with stationary regressors. To achieve estimation optimality, we further suggest a kernel mode-based two-step estimation procedure for estimating the stationary component. For numerically solving the model, we recommend a mode expectation-maximization algorithm and introduce a data-driven method for choosing the optimal bandwidths. We illustrate the finite sample performance of the developed estimators through Monte Carlo simulations and a real data application.