  For temporal regularly spaced datasets, a lot of methods are available and
the properties of these methods are extensively investigated. Less research has
been performed on irregular temporal datasets subject to measurement error with
complex dependence structures, while this type of datasets is widely available.
In this paper, the performance of kernel smoother for trend and its derivatives
is considered under dependent measurement errors and irregularly spaced
sampling scheme. The error processes are assumed to be subordinated Gaussian
long memory processes and have varying marginal distributions. The functional
central limit theorem for the estimators of trend and its derivatives are
derived and bandwidth selection problem is addressed.
