Convergence rate of Peng’s law of large numbers under sublinear expectations

“…Remark 2.11 Recently, Fang et al [4], Song [17] and Hu et al [7] obtained the convergence rate of (7) under higher moment conditions. If we further assume that Ê[X 2 1 ] < ∞ in Theorem 2.10, then we have…”

Section: Preliminaries Of Sublinear Expectation Theorymentioning

confidence: 99%

Maximum Likelihood Estimation for Maximal Distribution under Sublinear Expectation

Li¹,

Liu²,

Lu³

2023

Preprint

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Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We find the maximum likelihood estimator for the parameters of the maximal distribution via the solution of the associated minimax problem, which coincides with the optimal unbiased estimation given by Jin and Peng [8]. A general estimation method for samples with dependent structure is also provided. This result provides a theoretical foundation for the estimator of upper and lower variances, which is widely used in the G-VaR prediction model in finance.

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“…By the representation theorem of sublinear expectation (cf. [10,11,12]), there exists P on (R 2 , B(R 2 )) defined by…”

Section: Remark 44 This Definition Of Independence Is More General Th...mentioning

confidence: 99%

On the functional central limit theorem with mean-uncertainty

Li¹

2022

Preprint

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We introduce a new basic model for independent and identical distributed sequence on the canonical space (R N , B(R N )) via probability kernels with model uncertainty. Thanks to the well-defined upper and lower variances, we obtain a new functional central limit theorem with mean-uncertainty by the means of martingale central limit theorem and stability of stochastic integral in the classical probability theory. Then we extend it from the canonical space to the general sublinear expectation space. The corresponding proofs are purely probabilistic and do not rely on the nonlinear partial differential equation.

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Convergence rate of Peng’s law of large numbers under sublinear expectations

Cited by 9 publications

References 13 publications

Stein’s method for the law of large numbers under sublinear expectations

Stein’s method for the law of large numbers under sublinear expectations

Maximum Likelihood Estimation for Maximal Distribution under Sublinear Expectation

On the functional central limit theorem with mean-uncertainty

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