The research will deal with asymptotic problems in nonparametric inference. For inference on regression, due to the possibility of heavy-tailed residual distribution, regression is viewed in more general way than conditional expectation. Regression estimation with homogeneous residuals and various generalizations of the well-known Theil estimator will be sought. Inference on autoregressive processes with heavy-tailed residuals is part of such problems as well. Kernel and nearest neighbor methods will be used for estimation of a conditional quantile function. The important issue in these methods is the choice of the smoothing parameter. Other topics of study will include inference on linear regression based on truncated and censored data, use of covariate information via nonparametric regression in observational studies, methods for parallel regression, non- parallel regression and tests of parallelity.
