Postgraduate Seminar: Wishart -- Kink estimation in stochastic regression with dependent errors and predictors

In this talk we study the estimation of the location of jump points in the first
derivative (referred to as kinks) of a regression function $\mu$ in two random design
models with different long-range dependent (LRD) structures.  The method is based on the
so called zero-crossing technique and makes use of a high-order kernel smoothing
approach.  The rate of convergence of the estimator is contingent on the level of
dependence and the smoothness of the regression function $\mu$.  In one of the models,
the convergence rate is the same as the minimax rate for kink estimation in the fixed
design scenario with i.i.d.  errors which suggests that the method is optimal in the
minimax sense.  Time permitting, the Wavelet-Deconvolution approach to a similar problem
will be discussed which has potential for further applications by estimating the
location of jumps in higher order derivatives of $\mu$ (not just the first derivative).