We propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression model. Asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence as univariate function estimation. For the...

Generalized additive models (GAM) are multivariate nonparametric regressions for non-Gaussian responses including binary and count data. We propose a spline-backfitted kernel (SBK) estimator for the component functions. Our results are for weakly dependent data and we prove oracle efficiency....

For over a decade, nonparametric modelling has been successfully applied to study nonlinear structures in financial time series. It is well known that the usual nonparametric models often have less than satisfactory performance when dealing with more than one lag. When the mean has an additive...

Additive modelling has been widely used in nonparametric regression to circumvent the "curse of dimensionality", by reducing the problem of estimating a multivariate regression function to the estimation of its univariate components. Estimation of these univariate functions, however, can suffer...

Additive modelling is known to be useful for multivariate nonparametric regression as it reduces the complexity of problem to the level of univariate regression. This usefulness could be compromised if the data set was contaminated by outliers whose detection and removal are particularly...

We consider a varying coefficient regression model for sparse functional data, with time varying response variable depending linearly on some time independent covariates with coefficients as functions of time dependent covariates. Based on spline smoothing, we propose data driven simultaneous...

In spite of the widespread use of generalized additive models (GAMs), there is no well established methodology for simultaneous inference and variable selection for the components of GAM. There is no doubt that both, inference on the marginal component functions and their selection, are...

Longitudinal data analysis is a central piece of statistics. The data are curves and they are observed at random locations. This makes the construction of a simultaneous confidence corridor (SCC) (confidence band) for the mean function a challenging task on both the theoretical and the practical...