Asymptotic optimality of the bayes estimator in models differentiable in quadratic mean

In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

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Hierarchical Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality and Error Bounds

SSRN Electronic Journal ◽

10.2139/ssrn.1125453 ◽

1998 ◽

Cited By ~ 4

Author(s):

Suresh Sethi ◽

Hanqin Zhang ◽

Qing Zhang

Keyword(s):

Production Planning ◽

Error Bounds ◽

Average Cost ◽

Manufacturing System ◽

Asymptotic Optimality ◽

Hierarchical Production Planning ◽

Long Run

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Constant Job-Allowance Policies for Appointment Scheduling: Asymptotic Optimality and Numerical Analysis

SSRN Electronic Journal ◽

10.2139/ssrn.3133508 ◽

2018 ◽

Author(s):

Shenghai Zhou ◽

Yichuan Ding ◽

Woonghee Tim Huh ◽

Guohua Wan

Keyword(s):

Numerical Analysis ◽

Asymptotic Optimality ◽

Appointment Scheduling

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Complete subset averaging with many instruments

Econometrics Journal ◽

10.1093/ectj/utaa033 ◽

2020 ◽

Author(s):

Seojeong Lee ◽

Youngki Shin

Keyword(s):

Demand Function ◽

Simulation Experiment ◽

Mean Squared Error ◽

Asymptotic Optimality ◽

Weighted Average ◽

Subset Size ◽

Extensive Simulation ◽

Squared Error ◽

Many Instruments ◽

Class Of Estimators

Summary We propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weighted average over a complete subset with k instruments among K available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size k by the Nagar (1959) expansion. The subset size is chosen by minimising the sample counterpart of the approximate MSE. We show that this method achieves asymptotic optimality among the class of estimators with different subset sizes. To deal with averaging over a growing set of irrelevant instruments, we generalise the approximate MSE to find that the optimal k is larger than otherwise. An extensive simulation experiment shows that the CSA-2SLS estimator outperforms the alternative estimators when instruments are correlated. As an empirical illustration, we estimate the logistic demand function in Berry et al. (1995) and find that the CSA-2SLS estimate is better supported by economic theory than are the alternative estimates.

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Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

Monte Carlo Methods and Applications ◽

10.1515/mcma-2020-2062 ◽

2020 ◽

Vol 26 (2) ◽

pp. 131-161

Author(s):

Florian Bourgey ◽

Stefano De Marco ◽

Emmanuel Gobet ◽

Alexandre Zhou

Keyword(s):

Monte Carlo ◽

Lower Bounds ◽

Asymptotic Optimality ◽

Upper Bounds ◽

Upper And Lower Bounds ◽

Independent Random Variables ◽

Outer Function ◽

Control Problems ◽

Multilevel Monte Carlo ◽

Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

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