The problem considered here is that of using a data-driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter. In contrast to other papers on this subject, we consider models with heteroskedastic errors. The results apply to model selection...

We consider a diffusion process (X <Subscript> t </Subscript>)<Subscript> t ≥ 0</Subscript>, with drift b(x) and diffusion coefficient σ(x). At discrete times t <Subscript> k </Subscript> = k δ for k from 1 to M, we observe noisy data of the sample path, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${Y_{k\delta}=X_{k\delta}+\varepsilon_{k}}$$</EquationSource > </InlineEquation> . The random variables <InlineEquation ID="IEq2"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation></subscript></subscript></subscript>

This research focuses to develop some new techniques on statistical learning including methodology, computation and application. We also developed statistical quantification in nanomaterials. For a large number of random variables with temporal or spatial structures, we proposed shrink estimates...

In this paper we survey the most recent advances in supervised machine learning and highdimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention to penalized regressions and ensemble of models. The...

In this paper we survey the most recent advances in supervised machine learning and highdimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention to penalized regressions and ensemble of models. The...