Nonparametric estimation for dependent data with an
application to panel time series
In this paper we consider nonparametric estimation for dependent data,
where the observations do not necessarily come from a linear process.
We study density estimation and also discuss
associated problems in nonparametric regression using the 2-mixing
dependence measure. We compare the results under 2-mixing with
those derived under the assumption that the process is linear.
In the context of panel time series where one
observes data from several individuals, it is often too strong to
assume the joint linearity of
processes. Instead the methods developed in this paper enable us to
quantify the dependence through 2-mixing which allows for nonlinearity.
We propose an
estimator of the panel mean function and obtain its rate of convergence. We
show that under certain conditions the rate of convergence can be improved by
allowing the number of individuals in the panel to increase with time.