Ito-Ventzel's formula for semimartingales, asymptotic properties of mle and recursive estimation

Lazrieva, N.; Toronjadze, T.

doi:10.1007/bfb0038950

Cited by 8 publications

(6 citation statements)

References 3 publications

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“…to construct an estimator which is "asymptotically equivalent" to the MLE (see also [9] and [12]). Motivated by the above argument, one can consider a class of estimatorŝ…”

Section: Stochastic Approximation Type Estimation Algorithmsmentioning

confidence: 99%

Efficient on-line estimation of autoregressive parameters

Sharia

2010

Math. Meth. Stat.

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New procedures for estimating autoregressive parameters in AR(m) models are proposed. The proposed method allows for incorporation of auxiliary information into the estimation process and, under certain regularity conditions are consistent and asymptotically efficient. Also, these procedures are naturally on-line and do not require storing all the data. Theoretical results are presented in the case when m = 1. Two important particular cases are considered in details: linear procedures and likelihood procedures with the LS truncations. A specific example is also presented to briefly discuss some practical aspects of applications of the procedures of this type.

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“…to construct an estimator which is "asymptotically equivalent" to the MLE (see also [9] and [12]). Motivated by the above argument, one can consider a class of estimatorŝ…”

Section: Stochastic Approximation Type Estimation Algorithmsmentioning

confidence: 99%

Efficient on-line estimation of autoregressive parameters

Sharia

2010

Math. Meth. Stat.

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“…Recursive estimation procedure for MLE. In [18] an heuristic algorithm was proposed for the construction of recursive estimators of unknown parameter θ asymptotically equivalent to the maximum likelihood estimator (MLE). This algorithm was derived using the following reasons: Consider the MLE θ = ( θ t ) t≥0 , where θ t is a solution of estimational equation L t (θ) = 0.…”

Section: Recursive Parameter Estimation Procedures For Statistical Mo...mentioning

confidence: 99%

“…In 1987 by N. Lazrieva and T. Toronjadze an heuristic algorithm of a construction of the recursive parameter estimation procedures for statistical models associated with semimartingales (including both discrete and continuous time semimartingale statistical models) was proposed [18]. These procedures could not be covered by the generalized stochastic approximation algorithm proposed by Melnikov, while in i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Semimartingale stochastic approximation procedure and recursive estimation

2008

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The semimartingale stochastic approximation procedure, namely, the Robbins-Monro type SDE is introduced which naturally includes both generalized stochastic approximation algorithms with martingale noises and recursive parameter estimation procedures for statistical models associated with semimartingales. General results concerning the asymptotic behaviour of the solution are presented. In particular, the conditions ensuring the convergence, rate of convergence and asymptotic expansion are established. The results concerning the Polyak weighted averaging procedure are also presented.1991 Mathematics Subject Classification. 62L20, 60H10, 60H30. t 0 E W (s, x, u s )(µ − ν)(ds, dx) (in case 3 • ) provided the latters are well-defined.Consider the following semimartingale stochastic differential equationWe call SDE (0.1) the Robbins-Monro (PM) type SDE if the drift coefficient H t (u), t ≥ 0, u ∈ R 1 satisfies the following conditions: for all t ∈ [0, ∞) P -a.s. (A)H t (0) = 0,The question of strong solvability of SDE (0.1) is well-investigated (see, e.g., [8], [9], [13]).

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“…In general, the following heuristic argument can be used to establish a possible form of an approximate recursive relation (see also Jurečková and Sen (1996), Khas'minskii and Nevelson (1972), Lazrieva and Toronjadze (1987)). Since θn is defined as a root of the estimating equation (1.2), denoting the left hand side of (1.2) by M n (v) we have M n ( θn ) = 0 and M n−1 ( θn−1 ) = 0.…”

Section: Introductionmentioning

confidence: 99%

Recursive parameter estimation: asymptotic expansion

Sharia

2008

Ann Inst Stat Math

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We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any preliminary restrictions on the probabilistic nature of the observation process and cover a wide class of nonlinear recursive procedures. In this paper we study asymptotic behaviour of the recursive estimators. The results of the paper can be used to determine the form of a recursive procedure which is expected to have the same asymptotic properties as the corresponding non-recursive one defined as a solution of the corresponding estimating equation.

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Ito-Ventzel's formula for semimartingales, asymptotic properties of mle and recursive estimation

Cited by 8 publications

References 3 publications

Efficient on-line estimation of autoregressive parameters

Efficient on-line estimation of autoregressive parameters

Semimartingale stochastic approximation procedure and recursive estimation

Recursive parameter estimation: asymptotic expansion

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