Non-parametric Analysis of Covariance – The Case of Inhomogeneous and Heteroscedastic Noise

Abstract.  The purpose of this paper was to propose a procedure for testing the equality of several regression curves f _i in non-parametric regression models when the noise is inhomogeneous and heteroscedastic, i.e. when the variances depend on the regressor and may vary between groups. The presented approach is very natural because it transfers the maximum likelihood statistic from a heteroscedastic one-way analysis of variance to the context of non-parametric regression. The maximum likelihood estimators will be replaced by kernel estimators of the regression functions f _i . It is shown that the asymptotic distribution of the obtained test-statistic is nuisance parameter free. Asymptotic efficiency is compared with a test of Dette & Neumeyer [Annals of Statistics (2001) Vol. 29, 1361–1400] and it is shown that the new test is asymptotically uniformly more powerful. For practical purposes, a bootstrap variant is suggested. In a simulation study, level and power of this test will be briefly investigated and compared with other procedures. In summary, our theoretical findings are supported by this study. Finally, a crop yield experiment is reanalysed.     

AN ECONOMETRIC ANALYSIS OF CHARITABLE GIVING WITH INTERDEPENDENT PREFERENCES

Many economists and social scientists have conjectured that individual gifts to charity may be interdependent. This paper explores empirically how an individual's charitable contributions may be affected by the giving of others in a "reference group" of similar individuals. We find modest evidence of interdependence of preferences through these reference groups, although the aggregate effects are not large. Hence, we conclude that the inferences from standard models, which ignore interdependence of preferences, are not likely to be misleading. ( JEL H31, H41, D12)