This paper presents a generalization of the minimax state estimation approach for singular linear Differential-Algebraic Equations (DAE) with uncertain but bounded input and observation’s noise. We apply generalized Kalman Duality principle to DAE in order to represent the minimax estimate as a solution of a dual control problem for adjoint DAE. The latter is then solved converting the adjoint ...

Discussion Papers are a series of manuscripts in their draft form. They are not intended for circulation or distribution except as indicated by the author. For that reason Discussion Papers may not be reproduced or distributed without the written consent of the author. The estimation of a linear combination of several restricted location parameters is addressed from a decision-theoretic point o...

For a long time, lower bounds on the difficulty of estimation have been constructed by showing that estimation was difficult even in certain 1-dimensional subproblems. The logical extension of this is to identify hardest one dimensional subproblems and to ask whether these are, either exactly or approximately, as difficult as the full problem. We do this in three settings: estimating linear fun...

This paper deals with the minimax parameter estimation of nonlinear parametric models from experimental data. Taking advantage of the special structure of the minimax problem, a new e¢cient and reliable algorithm based on interval constraint propagation is proposed. As an illustration, the ill-conditioned problem of estimating the parameters of a two-exponential model is considered.

We consider the estimation of regression coefficients in a high-dimensional linear model. A lower bound of the minimax `q risk is provided for regression coefficients in `r balls, along with a minimax lower bound for the tail of the `q loss. Under certain conditions on the design matrix and penalty level, we prove that these minimax convergence rates are attained by both the Lasso and Dantzig e...

In the estimation problem of unknown variance of a multivariate normal distribution, a new class of minimax estimators is obtained. It is noted that a sequence of estimators in our class converges to the Stein’s truncated estimator.

This paper constructs bounds on the minimax risk under loss functions when statistical estimation is performed in a distributed environment and with communication constraints. We treat this problem using techniques from information theory and communication complexity. In many cases our bounds rely crucially on metric entropy conditions and the classical reduction from estimation to testing. A n...

Abstract: Consider the standard Gaussian linear regression model Y = Xθ0 + ǫ, where Y ∈ R is a response vector and X ∈ R is a design matrix. Numerous work have been devoted to building efficient estimators of θ0 when p is much larger than n. In such a situation, a classical approach amounts to assume that θ0 is approximately sparse. This paper studies the minimax risks of estimation and testing...