Variance Reduction in Smoothing Splines

Abstract.  We develop a variance reduction method for smoothing splines. For a given point of estimation, we define a variance-reduced spline estimate as a linear combination of classical spline estimates at three nearby points. We first develop a variance reduction method for spline estimators in univariate regression models. We then develop an analogous variance reduction method for spline estimators in clustered/longitudinal models. Simulation studies are performed which demonstrate the efficacy of our variance reduction methods in finite sample settings. Finally, a real data analysis with the motorcycle data set is performed. Here we consider variance estimation and generate 95% pointwise confidence intervals for the unknown regression function.     

Students' Views on the Relationship between Religion and Science: Analyses of Results from a Comparative Survey*

Deux enquêtes ont été effectuées auprès d'étudiants de deux universitiés canadiennes sur leurs perceptions des relations entre la religion, la science et le sens de la vie. Les données démontrent que, tandis que les étudiants pensent régulièrement à la signification de la vie, leurs opinions sur la religion par rapport à la science ne laissent voir que de bas niveaux de corrélation. Les étudiants ont indiqué que leur plus grande préoccupation par rapport au sens de la vie était due à leur famille et à leurs amis. Dans l'ensemble, les données suggèrent que les étudiants considèrent la religion et la science comme des entités indépendantes, mais seulement en ce qui concerne la part qu'elles occupent dans la vie des individus et dans les affaires mondiales.
Students at two distinctly different Canadian universities were surveyed about their perceptions of the relationship between religion, science, and thinking about the meaning of life. The data show that while students regularly think about the latter, their views on religion and science show only low levels of correlation with each other. Students indicated that their greatest insights into the meaning of life came from family and friends. Overall, the data suggest that students view religion and science as independent entities, both with respect to the part that these play in the life of individuals and in world affairs.     

Is a Questionnaire Necessary in a Second Mailing?

Current Research This section of POQ is reserved for brief reportsof research in progress, discussions of unresolved problems,methodological studies, and public opinion data not extensivelyanalyzed or interpreted. Succinct case histories are welcomed,as well as hypotheses and insights that may be useful to otherstudents of public opinion. Usually, material in this sectionis shorter, more informal, and more tentative than in precedingpages.