On multi-step MLE-process for Markov sequences

Kutoyants, Yury A.; Motrunich, Anastasia

doi:10.1007/s00184-015-0574-4

Cited by 16 publications

(16 citation statements)

References 13 publications

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“…Indeed, it can be shown (see Kamatani and Uchida (2015) or Kutoyants and Motrunich (2016)) that for a n δ/2 -consistent initial sequence of guess estimators (with 1 2 < δ ≤ 1) and a Lipshitz Fisher information matrix, the sequence of Le Cam's one-step estimators is also consistent, asymptotically normal and efficient (in the Fisher sense). In this setting, for a initial sequence which is neither asymptotically rate nor variance efficient, the new sequence is asymptotically rate and variance efficient.…”

Section: Pólya (Negative Binomial)mentioning

confidence: 99%

OneStep : Le Cam's One-step Estimation Procedure

Brouste¹,

Dutang²,

Mieniedou³

2021

The R Journal

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The OneStep package proposes principally an eponymic function that numerically computes Le Cam's one-step estimator, which is asymptotically efficient and can be computed faster than the maximum likelihood estimator for large datasets. Monte Carlo simulations are carried out for several examples (discrete and continuous probability distributions) in order to exhibit the performance of Le Cam's one-step estimation procedure in terms of efficiency and computational cost on observation samples of finite size.

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Section: Pólya (Negative Binomial)mentioning

confidence: 99%

OneStep : Le Cam's One-step Estimation Procedure

Brouste¹,

Dutang²,

Mieniedou³

2021

The R Journal

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“…. , n − 1 the similar multi-step MLE-process provides asymptotically efficient estimator process too [14]. The construction of the multi-step MLE-processes can be done in the case of inhomogeneous Poisson processes, i.i.d.…”

Section: Examplementioning

confidence: 99%

On the multi-step MLE-process for ergodic diffusion

Kutoyants

2017

Stochastic Processes and their Applications

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We propose a new method of the construction of the asymptotically efficient estimator-processes asymptotically equivalent to the MLE and the same time much more easy to calculate. We suppose that the observed process is ergodic diffusion and that there is a learning time interval of the length negligeable with respect to the whole time of observations. The preliminary estimator obtained after the learning time is then used in the construction of one-step and twostep MLE processes. We discuss the possibility of the applications of the proposed estimation procedure to several other observations models.

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“…, X k ), is easy to calculate and is asymptotically efficient because it is asymptotically equivalent to the MLE. For the details see Kutoyants and Motrunich (2016).…”

Section: To Estimate Y T We Need An Estimator Which Is Constructed Bmentioning

confidence: 99%

On approximation of BSDE and multi-step MLE-processes

Kutoyants

2016

Probab Uncertain Quant Risk

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which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. AbstractWe consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case. We suppose that the forward equation depends on some unknown finite-dimensional parameter. This approximation is based on the solution of the partial differential equations and multi-step estimator-processes of the unknown parameter. As the model of observations of the forward equation we take a diffusion process with small volatility. First we establish a lower bound on the errors of all approximations and then we propose an approximation which is asymptotically efficient in the sense of this bound. The obtained results are illustrated on the example of the Black and Scholes model.

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On multi-step MLE-process for Markov sequences

Cited by 16 publications

References 13 publications

OneStep : Le Cam's One-step Estimation Procedure

OneStep : Le Cam's One-step Estimation Procedure

On the multi-step MLE-process for ergodic diffusion

On approximation of BSDE and multi-step MLE-processes

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