On Non Parametric Regression and Panel Unit Root Testing

Abstract: In this thesis, two different issues in econometrics are studied, the estimation of regression coefficients and the non-stationartiy analysis in a panel setting.Regarding the first topic, we study a set of measure of location-based estimators (MLBEs) for the slope parameter in a linear regression model with a single stochastic regressor. The median-unbiased MLBEs are interesting as they can be robust to heavy-tailed and, hence, preferable to the ordinary least squares estimator (LSE) in such situations. Two cases, symmetric stable regression and contaminated normal regression, are considered as we investigate the statistical properties of the MLBEs. In addition, we illustrate how our results can be extended to include certain heteroscedastic regressions.There are three papers concerning the second part. In the first paper, we propose a novel way to test the unit roots in the panel setting. The new tests are based on the observation that the trajectory of the cross sectional sample variance behaves differently for stationary than for non-stationary processes. Three different test statistics are proposed. The limiting distributions are derived and the small sample properties are studied by simulations. In the remaining papers, we focus on the studies of the block bootstrap panel unit root tests proposed by Palm, Smeekes and Urbain (2011) which aims at dealing with a rather general cross-sectional dependency structure. One paper studies the robustness of PSU tests by a comparison with two representative tests from the second generation panel unit root tests. In another paper, we generalized the block bootstrap panel unit root tests in the sense of considering the deterministic terms in the model. Two different methods to deal with the deterministic terms are proposed and the asymptotic validity of bootstrap tests under the main null hypothesis is theoretically checked. The small sample properties are studied by simulations.