On Universally Efficient Parameter Estimation in Parametric Models and Universal Data Compression

It is well known that classical parameter estimation methods rely on the knowledge of the parametric form of the noise density (e. g. Gaussian density). We study several parameter estimation problems, associated with location model, linear regression model and the autoregressive model, for the case where the noise probability density function is completely unknown. We say that an estimator is universal asymptotically efficient if it does not depend on this unknown density function, and at the same time, it attains asymptotically the Cramer-Rao lower bound, uniformly for every well-behaved density function.