On the recursive parameter estimation in the general discrete time statistical model

Sharia, Teo

doi:10.1016/s0304-4149(97)00098-7

Cited by 11 publications

(12 citation statements)

References 10 publications

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“…The second approach presented exploits the stochastic version of the Kronecker Lemma. This approach is employed in [39] for the discrete time case under the assumption (2.2.23). The comparison of the results obtained in this section with those obtained before is also presented.…”

Section: 2mentioning

confidence: 99%

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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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Section: 2mentioning

confidence: 99%

“…In Example 2 we show that the recursive parameter estimation procedure for discrete time general statistical models can also be embedded in stochastic approximation procedure given by (0.1). This procedure was studied in [39] in a full capacity.…”

Section: Introductionmentioning

confidence: 99%

Semimartingale stochastic approximation procedure and recursive estimation

2008

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“…Asymptotic behaviour of this type of procedures for non i.i.d. models was studied by a number of authors, see e.g., [7], [9], [18], [24] - [27]. Results in [27] show that to obtain an estimator with asymptotically optimal properties, one has to consider a state-dependent matrix-valued random step-size sequence.…”

Section: Introductionmentioning

confidence: 99%

Truncated stochastic approximation with moving bounds: convergence

Sharia

2014

Stat Inference Stoch Process

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In this paper we propose a wide class of truncated stochastic approximation procedures with moving random bounds. While we believe that the proposed class of procedures will find its way to a wider range of applications, the main motivation is to accommodate applications to parametric statistical estimation theory. Our class of stochastic approximation procedures has three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and dynamically changing random regression function. We establish convergence and consider several examples to illustrate the results.

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“…In particular, Englund et al (1989) give an asymptotic representation results for certain type of X n processes. In Sharia (1998), theoretical results on convergence, rate of convergence and the asymptotic representation are given under certain regularity and ergodicity assumptions on the model, in the one-dimensional case with ψ n (x, θ) = ∂ ∂θ logf n (x, θ) (see also Campbell (1982), Sharia (1992), and Lazrieva et al (1997)). …”

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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On the recursive parameter estimation in the general discrete time statistical model

Cited by 11 publications

References 10 publications

Semimartingale stochastic approximation procedure and recursive estimation

Semimartingale stochastic approximation procedure and recursive estimation

Truncated stochastic approximation with moving bounds: convergence

Recursive parameter estimation: asymptotic expansion

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