Minimax estimation in generalized linear uncertain-stochastic model

Pankov, A. R.; Semenikhin, K. V.

doi:10.1109/cdc.1998.757917

Cited by 3 publications

(7 citation statements)

References 4 publications

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“…As it is known [22,31], for a singular observation model a minimax estimate is not unique. This makes it reasonable to introduce the next concept.…”

Section: Minimax Estimation Problemmentioning

confidence: 97%

“…This aim is achieved by means of the Tikhonov regularization techniques [7,8,17,22,27]. Combination of the methods of dual optimization and Tikhonov regularization provides a unified approach to designing efficient algorithms of minimax robust identification for any linear multivariate system with mixed a priori uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…(a) the models involving only random variables with partially known nondegenerate distributions [2,15,20,26,31]; (b) the models with uncertain but bounded nonrandom parameters and disturbances [5,7,12,16,18,19].…”

Section: Introductionmentioning

confidence: 99%

“…20) where x is a scalar nonrandom parameter to be estimated given the observations y = col[y 1 , . .…”

mentioning

confidence: 99%

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Minimax estimation for singular linear multivariate models with mixed uncertainty

Pankov

Siemenikhin

2007

Journal of Multivariate Analysis

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The problem of minimax estimation is examined for the linear multivariate statistically indeterminate observation model with mixed uncertainty. The a priori information on the distributions of model parameters is formulated in terms of second-order moment characteristics. It is shown that in the regular case the minimax estimate is defined explicitly via the solution of the dual optimization problem. For singular models, the method of dual optimization is developed by means of using the Tikhonov regularization techniques. Several particular cases which are widely used in practice are also considered.

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“…As it is known [22,31], for a singular observation model a minimax estimate is not unique. This makes it reasonable to introduce the next concept.…”

Section: Minimax Estimation Problemmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…20) where x is a scalar nonrandom parameter to be estimated given the observations y = col[y 1 , . .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Minimax estimation for singular linear multivariate models with mixed uncertainty

Pankov

Siemenikhin

2007

Journal of Multivariate Analysis

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“…Duality theory and convex analysis methods have become the foundation for minimax estimation and control algorithms [2,[19][20][21]. In this work, we use the dual optimization method [22][23][24][25][26][27] to solve a multidimensional optimization minimax estimation problem. This approach has proven effective in case when the dimensionality of the vector of unknown parameters or uncertain characteristics is significantly less than the number of observations.…”

Section: Introductionmentioning

confidence: 99%

Minimax estimation methods under ellipsoidal constraints

Mamaev

Semenikhin

2013

Autom Remote Control

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Minimax Estimation in Regression under Sample Conformity Constraints

Борисов

2021

Mathematics

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The paper is devoted to the guaranteeing estimation of parameters in the uncertain stochastic nonlinear regression. The loss function is the conditional mean square of the estimation error given the available observations. The distribution of regression parameters is partially unknown, and the uncertainty is described by a subset of probability distributions with a known compact domain. The essential feature is the usage of some additional constraints describing the conformity of the uncertain distribution to the realized observation sample. The paper contains various examples of the conformity indices. The estimation task is formulated as the minimax optimization problem, which, in turn, is solved in terms of saddle points. The paper presents the characterization of both the optimal estimator and the set of least favorable distributions. The saddle points are found via the solution to a dual finite-dimensional optimization problem, which is simpler than the initial minimax problem. The paper proposes a numerical mesh procedure of the solution to the dual optimization problem. The interconnection between the least favorable distributions under the conformity constraint, and their Pareto efficiency in the sense of a vector criterion is also indicated. The influence of various conformity constraints on the estimation performance is demonstrated by the illustrative numerical examples.

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Minimax estimation in generalized linear uncertain-stochastic model

Cited by 3 publications

References 4 publications

Minimax estimation for singular linear multivariate models with mixed uncertainty

Minimax estimation for singular linear multivariate models with mixed uncertainty

Minimax estimation methods under ellipsoidal constraints

Minimax Estimation in Regression under Sample Conformity Constraints

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