On guaranteed parameter estimation of a multiparameter linear regression process

Abstract

On guaranteed parameter estimation of a multiparameter linear regression process 1;2 we u uhler yheslv eF siliev snstitute of wthemtis heprtment of epplied wthemtis rumoldt niversity ferlin nd gyernetis nter den vinden TD hEIHHWW omsk tte niversity ferlinD qermny venin QTD TQRHSH omskD ussi Abstract his pper presents sequentil estimtion proedure for the unknown prmeters of ontinuousEtime stohsti liner regression proessF es exmples the sequenE til estimtion prolem of two dynmi prmeters in stohsti liner systems with memory nd in utoregressive proesses is solvedF he estimtion proedure is sed on the lest squres method with weights nd yields estimtors with gurnteed E ury in the sense of the L q norm for xed q ! PF he proposed proedure works in the mentioned exmples for ll possile vlues of unknown dynmi prmeters on the plne R P for the utoregressive proesses nd on the plne R P with the exeption of some lines for the liner stohsti dely equtionsF he symptoti ehvior of the durtion of oservtions is determinedF he generl estimtion proedure is designed for twoE or moreEprmetri modelsF st is shownD tht the proposed proedure n e pplied to the sequentil prmeter estimtion prolem of ne stohsti dely dierentil equtions nd utoregresE sive proesses of n ritrry orderF

On Guaranteed Parameter Estimation of Stochastic Delay Differential Equations by Noisy Observations

“…Then we shall define, similar to [11,13,14,16], the final sequential estimation plan, which works in Θ as a sequential plan with the smallest duration of observations.…”

“…We shall construct the sequential estimation procedure of the parameter ϑ on the basis of the correlation method in the cases Θ 1 , Θ 4 (similar to [12,14,15]) and on the basis of correlation estimators with weights in the cases Θ 2 ∪ Θ 3 . The last cases and Θ 13 are new.…”

“…The set Θ is defined to be the intersection of the set Θ with an arbitrary but fixed ball B 0,R ⊂R 2 . Sequential estimation problem has been solved for sets Θ of a different structure in [7]- [9], [11,13,14,16] by observations of the process (1) and in [10,12,15] -by noisy observations (2).…”

“…The general sequential estimation problem for all ϑ =( a, b) ′ from R 2 except of two lines was solved in [13,14,16] for the equation (1) based on the observations of X(·).…”

“…In this chapter the sequential estimation method developed in [10,12] for the system (1), (2) is extended to the case, considered by [13,14,16] for the equation (1) (as already mentioned, for all ϑ from R 2 except of two lines for the observations without noises).…”