Tracking control of uncertain systems

Deals with the problem of designing output tracking controllers for uncertain systems. The systems we consider may be non-minimum phase but are restricted to be linear. The problem is motivated by control applications where a desired output trajectory is specified, and the corresponding input to the system is to be found

Asymptotic equivalence of discretely observed diffusion processes and their Euler scheme: small variance case

This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models on the other side. The time horizon $T$ is kept fixed and both the cases of discrete and continuous observation of the path are treated. We allow non constant diffusion coefficient, bounded but possibly tending to zero. The asymptotic equivalences are established by constructing explicit equivalence mappings.Comment: 21 page

Optimal nonparametric estimation of the density of regression errors with finite support

Adaptation, Error depending on predictor, Heteroscedasticity, Minimax, Pinsker oracle,

Oracle inequality for conditional density estimation and an actuarial example

Dimension reduction, Fixed and random design, MISE, Nonparametric regression,

A Study of Blockwise Wavelet Estimates Via Lower Bounds for a Spike Function

A blockwise shrinkage is a popular adaptive procedure for non-parametric series estimates. It possesses an impressive range of asymptotic properties, and there is a vast pool of blocks and shrinkage procedures used. Traditionally these estimates are studied via upper bounds on their risks. This article suggests the study of these adaptive estimates via non-asymptotic lower bounds established for a spike underlying function that plays a pivotal role in the wavelet and minimax statistics. While upper-bound inequalities help the statistician to find sufficient conditions for a desirable estimation, the non-asymptotic lower bounds yield necessary conditions and shed a new light on the popular method of adaptation. The suggested method complements and knits together two traditional techniques used in the analysis of adaptive estimates: a numerical study and an asymptotic minimax inference. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..