Abstracts 1.2 Panelized and Shrinkage Estimation in Partially Linear Models Nonparametric Tests of Hypotheses for Umbrella Alternatives Abstracts 1.2

S 1.2 S. EJAZ AHMED University of Windsor Panelized and Shrinkage Estimation in Partially Linear Models Panelized and shrinkage regression have been widely used in high-dimensional data analysis. Much recent work has been done on the study of penalized least square methods in linear models. In this talk, we consider an absolute penalty type estimator (APE) for partially linear models, which is an extension of the Lasso method for linear models. We also consider Stein-type and pretest semiparametric estimators for this model with potential irrelevant presence of nuisance variables. We establish the asymptotic results for shrinkage and pretest estimators. A Monte Carlo comparison of the proposed estimators is presented. The comparison shows that the shrinkage method performs better than the APE when the dimension of the restricted space is large. S. EJAZ AHMED AND MOHAMED AMEZZIAN University of Windsor, DePaul University Semiparametric Density Estimation We explore the usefulness of shrinkage strategy as a means of constructing semi-parametric density estimators. We investigate the properties of the shrinkage coefficient and study the optimality and limiting distribution of the new density estimator. We also devise a related test of goodness-of-fit about the density. Theoretical results are supported by an extensive simulation study MAYER ALVO University of Ottawa Nonparametric Tests of Hypotheses for Umbrella Alternatives A general method is proposed for constructing nonparametric tests of hypotheses for umbrella alternatives. Such alternatives arise in situations where the treatment effect changes in direction after reaching a peak. Our class of tests are based on the ranks of the observations. The general approach consists of defining two sets of rankings: the first is induced by the alternative and the other by the data itself. The test statistic measures the distance between the two sets. The asymptotic distributions are determined for some special cases of distances under both the null and the alternative hypothesis when the location of the peak is known or unknown. A limited simulation study shows that the tests have good power.