Sensitivity of normal-based triple sampling sequential point estimation to the normality assumption

Yousef, Ali; Kimber, Alan; Hamdy, H. I.

doi:10.1016/j.jspi.2013.03.027

Cited by 9 publications

(5 citation statements)

References 22 publications

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“…Others have introduced point estimation under some error loss functions or tried to improve the quality of inference like protecting the inference against type II error probability, studying the operating characteristic curve, or/and discussing the sensitivity of the three-stage sampling when the underline distribution departs away from normality. For details, see Costanzo et al [32], Hamdy et al [33], Son et al [34], Yousef et al [35], Hamdy et al [36], and Yousef [37,38].…”

Section: Three-stage Sequential Estimationmentioning

confidence: 99%

Three-Stage Sequential Estimation of the Inverse Coefficient of Variation of the Normal Distribution

Yousef

Hamdy

2019

Computation

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This paper sequentially estimates the inverse coefficient of variation of the normal distribution using Hall’s three-stage procedure. We find theorems that facilitate finding a confidence interval for the inverse coefficient of variation that has pre-determined width and coverage probability. We also discuss the sensitivity of the constructed confidence interval to detect a possible shift in the inverse coefficient of variation. Finally, we find the asymptotic regret encountered in point estimation of the inverse coefficient of variation under the squared-error loss function with linear sampling cost. The asymptotic regret provides negative values, which indicate that the three-stage sampling does better than the optimal fixed sample size had the population inverse coefficient of variation been known.

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Section: Three-stage Sequential Estimationmentioning

confidence: 99%

Three-Stage Sequential Estimation of the Inverse Coefficient of Variation of the Normal Distribution

Yousef

Hamdy

2019

Computation

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“…Let N be defined as in Equation 8and assume (A) holds, the asymptotic characteristics of the fine-tuning phase as ξ → ∞ we have (see Yousef et al [38]) 8, we can show that for any real k and as ξ → ∞…”

Section: Theorem 3 Under Assumption (A) and Using Equationmentioning

confidence: 93%

“…al. [38], Yousef [39], Hamdy et al [40] and Yousef [41]. Liu [42] used Hall's results to tackle hypothesis-testing problems for the mean of the normal distribution while Son et al [43] used the three-stage procedure to tackle the problem of testing hypotheses concerning shifts in the population normal mean with controlled Type II error probability.…”

Section: Three-stage Estimation Of the Mean And Variancementioning

confidence: 99%

Three-Stage Estimation of the Mean and Variance of the Normal Distribution with Application to an Inverse Coefficient of Variation with Computer Simulation

Yousef

Hamdy

2019

Mathematics

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This paper considers sequentially two main problems. First, we estimate both the mean and the variance of the normal distribution under a unified one decision framework using Hall’s three-stage procedure. We consider a minimum risk point estimation problem for the variance considering a squared-error loss function with linear sampling cost. Then we construct a confidence interval for the mean with a preassigned width and coverage probability. Second, as an application, we develop Fortran codes that tackle both the point estimation and confidence interval problems for the inverse coefficient of variation using a Monte Carlo simulation. The simulation results show negative regret in the estimation of the inverse coefficient of variation, which indicates that the three-stage procedure provides better estimation than the optimal.

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“…Meanwhile, Liu [33] extended Hall's results to tackle hypothesis-testing problems for the normal mean. Yousef [34] discussed the sensitivity of the normal-based triple sampling sequential point estimation to the normality assumption, considering a class of an absolutely continuous distribution whose absolute first six moments are assumed finite but unknown. After that, he generalized the study to find the second-order asymptotic coverage probability and the second-order characteristic operating function for the mean.…”

Section: Sequential Sampling Proceduresmentioning

confidence: 99%

Triple Sampling Inference Procedures for the Mean of the Normal Distribution When the Population Coefficient of Variation Is Known

2023

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This paper discusses the triple sampling inference procedures for the mean of a symmetric distribution—the normal distribution when the coefficient of variation is known. We use the Searls’ estimator as an initial estimate for the unknown population mean rather than the classical sample mean. In statistics literature, the normal distribution under investigation underlines almost all the natural phenomena with applications in many fields. First, we discuss the minimum risk point estimation problem under a squared error loss function with linear sampling cost. We obtained all asymptotic results that enhanced finding the second-order asymptotic risk and regret. Second, we construct a fixed-width confidence interval for the mean that satisfies at least a predetermined nominal value and find the second-order asymptotic coverage probability. Both estimation problems are performed under a unified optimal framework. The theoretical results reveal that the performance of the triple sampling procedure depends on the numerical value of the coefficient of variation—the smaller the coefficient of variation, the better the performance of the procedure.

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Sensitivity of normal-based triple sampling sequential point estimation to the normality assumption

Cited by 9 publications

References 22 publications

Three-Stage Sequential Estimation of the Inverse Coefficient of Variation of the Normal Distribution

Three-Stage Sequential Estimation of the Inverse Coefficient of Variation of the Normal Distribution

Three-Stage Estimation of the Mean and Variance of the Normal Distribution with Application to an Inverse Coefficient of Variation with Computer Simulation

Triple Sampling Inference Procedures for the Mean of the Normal Distribution When the Population Coefficient of Variation Is Known

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