Sequential Estimation of the Square of the Rayleigh Parameter

Tahir, Mohamed

doi:10.3844/jmssp.2014.275.280

Cited by 2 publications

(1 citation statement)

References 12 publications

(11 reference statements)

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“…Tahir [60] addressed a sequential procedure to tackle a point estimation problem for the Rayleigh distribution parameter square, subject to a weighted squared-error loss plus cost of sampling. He found a second-order asymptotic expansion for the incurred regret and found that the asymptotic regret is negative for a range of parameter values.…”

Section: Multistage Samplingmentioning

confidence: 99%

Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

et al. 2020

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This paper discusses the sequential estimation of the scale parameter of the Rayleigh distribution using the three-stage sequential sampling procedure proposed by Hall (Ann. Stat.1981, 9, 1229–1238). Both point and confidence interval estimation are considered via a unified optimal decision framework, which enables one to make the maximum use of the available data and, at the same time, reduces the number of sampling operations by using bulk samples. The asymptotic characteristics of the proposed sampling procedure are fully discussed for both point and confidence interval estimation. Since the results are asymptotic, Monte Carlo simulation studies are conducted to provide the feel of small, moderate, and large sample size performance in typical situations using the Microsoft Developer Studio software. The procedure enjoys several interesting asymptotic characteristics illustrated by the asymptotic results and supported by simulation.

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Section: Multistage Samplingmentioning

confidence: 99%

Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

et al. 2020

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Multistage Estimation of the Rayleigh Distribution Variance

et al. 2020

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In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure attains asymptotic second-order efficiency and asymptotic consistency. A series of Monte Carlo simulations were conducted to study the procedure’s performance as the optimal sample size increases. We found that the simulation results agree with the asymptotic results.

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Sequential Estimation of the Square of the Rayleigh Parameter

Cited by 2 publications

References 12 publications

Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

Multistage Estimation of the Rayleigh Distribution Variance

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