|Wavelets have been widely used lately in many areas such as physics, astronomy, biological
sciences and recently to statistics. The main goal of this dissertation is to provide
a new contribution to an important problem in statistics and particularly nonparametric
statistics, namely estimating the optimal score function from the data with unknown underlying
distribution. This problem naturally arises in nonparametric linear regression
models and could be important in order to have a better insight on more important and
actual problems in longitudinal and repeated measures analysis through mixed models.
Our approach in estimating the score function is to use suitable compactly supported
wavelets like the Daubechies, Symlets or Coi
ets family of wavelets. The smoothness
and time-frequency properties of these wavelets allow us to nd an asymptotically e -
cient estimator of the slope parameter of the linear model. Consequently, we are also able
to provide a consistent estimator of the asymptotic variance of the regression parameter.
For related mixed models, asymptotic relative efficiency is also discussed.