It has been a long history of using interactions in regression analysis to investigate alterations in covariate-effects on response variables. In this article, we aim to address two kinds of new challenges arising from the inclusion of such high-order effects in the regression model for complex data. The first kind concerns a situation where interaction effects of individual covariates are weak...

The paper considers nonparametric inference for quantile regression models with time-varying coefficients. The errors and covariates of the regression are assumed to belong to a general class of locally stationary processes and are allowed to be cross-correlated. Simultaneous confidence tubes (SCT) and integrated squared difference tests (ISDT) are proposed for simultaneous nonparametric infere...

We propose a functional random effect time-varying coefficient model to establish the dynamic relationship between the response and predictor variables in longitudinal data. This model allows us not only to interpret time-varying covariate effects, but also to depict random effects via time-varying profiles that are characterized by functional principal components. We develop the functional pro...

( ) ( ) ( ) t t / L L e 1 1 e t + − = ρ and 1 Y L − + = t t β α , that is, we investigate the nonlinear least squares estimator. Starting with the simplest case 0 = β , we find that ( ) ( ) ( ) 1 e 1 e t + − = α α ρ / which is just a constant so the estimator that minimizes the error sum of squares must be ( ) ( ) ( ) ρ ρ α ˆ / ˆ ˆ − + = 1 1 ln where ρ̂ is the usual regression estimate of (the c...

This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to embody a mixture of stochastic and determ...

Time-varying coefficient models are useful in longitudinal data analysis. Various efforts have been invested for the estimation of the coefficient functions, based on the least squares principle. Related work includes smoothing spline and kernel methods among others, but these methods suffer from the shortcoming of non-robustness. In this paper, we introduce a local M-estimation method for esti...