The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are: (1) the study is non-asymptotic, that is, the sample size is fixed and does not tend to infinity; (2) the parametric assumption is possibly...

This paper offers a new method for estimation and forecasting of the linear and nonlinear time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient parametric models, such as AR or GARCH, whose coefficients...

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are: (1) the study is non-asymptotic, that is, the sample size is fixed and does not tend to infinity; (2) the parametric assumption is possibly...

Given a random sample from some unknown density f0 : R → [0;∞) we devise Haar wavelet estimators for fo with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen, and Spokoiny (1997, Ann. Statist.)). We show that these estimators adapt to spatially...