Nonparametric and semiparametric estimation and testing.

This thesis deals with certain problems in nonparametric estimation and testing. In the first part of the thesis, we propose a method to improve nonparametric regression estimates of regression functions with a similar shape. This is achieved by first estimating the unknown parameters in the parametric relationship between the regression functions, and subsequently using the estimated transformation to pool the two data sets. The second part is concerned with nonparametric tests for serial independence. We extend an idea by Robinson (1991a) to use the Kullback-Leibler information criterion to measure the distance between the joint and marginal densities of consecutive observations in a stationary time series, and we also propose an entirely new test in which the joint and marginal characteristic functions of afore-mentioned observations are used.