On the estimation of skewness of a statistic using the jackknife and the bootstrap

Tu, Dongsheng; Zhang, L.

doi:10.1007/bf02925311

Cited by 11 publications

(5 citation statements)

References 12 publications

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“…Several authors have point out the essence of bootstrap techniques as an alternative method of conducting inference where the sample size is not large or sampling distributions are analytically intractable, due to nonlinearity or pre-testing, etc. [19,20]. 4 Some of the data can be retrieved from: http://www.economics.gr.…”

Section: Datamentioning

confidence: 99%

A conditional nonparametric analysis for measuring the efficiency of regional public healthcare delivery: An application to Greek prefectures

Halkos

Tzeremes

2011

Health Policy

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Section: Datamentioning

confidence: 99%

A conditional nonparametric analysis for measuring the efficiency of regional public healthcare delivery: An application to Greek prefectures

Halkos

Tzeremes

2011

Health Policy

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“…Stable predictions are not warranted in such circumstances. Small data spreads must obey normal statistics for a bootstrap solver to be accurate in its predictions (Good, 2005; Tu and Zhang, 1992). Moreover, bootstrap-based solutions rely on a representative sample.…”

Section: Discussionmentioning

confidence: 99%

“…The backlash due to the complexity in the thermostat lifecycle data is magnified by the unavoidable presence of skewness. Skewness spurs pervasive uncertainty contributions in bootstrap methods particularly in conditions where small data conditions prevail (Briggs, 2016; Chernick and LaBudde, 2011; Tu and Zhang, 1992). This severe asymmetry within each factor-setting is typified on the 10th percentile dataset as will illustrate in the Results section by individually box-plotting all eleven effects.…”

Section: Literature Reviewmentioning

confidence: 99%

QUALITY PAPERA new rapid and robust multi-factorial screening for low-percentile use-rate accelerated reliability analysis

Besseris

Tsarouhas

2021

IJQRM

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PurposeThe study aims to provide a quick-and-robust multifactorial screening technique for early detection of statistically significant effects that could influence a product's life-time performance.Design/methodology/approachThe proposed method takes advantage of saturated fractional factorial designs for organizing the lifetime dataset collection process. Small censored lifetime data are fitted to the Kaplan–Meier model. Low-percentile lifetime behavior that is derived from the fitted model is used to screen for strong effects. A robust surrogate profiler is employed to furnish the predictions.FindingsThe methodology is tested on a difficult published case study that involves the eleven-factor screening of an industrial-grade thermostat. The tested thermostat units are use-rate accelerated to expedite the information collection process. The solution that is provided by this new method suggests as many as two active effects at the first decile of the data which improves over a solution provided from more classical methods.Research limitations/implicationsTo benchmark the predicted solution with other competing approaches, the results showcase the critical first decile part of the dataset. Moreover, prediction capability is demonstrated for the use-rate acceleration condition.Practical implicationsThe technique might be applicable to projects where the early reliability improvement is studied for complex industrial products.Originality/valueThe proposed methodology offers a range of features that aim to make the product reliability profiling process faster and more robust while managing to be less susceptible to assumptions often encountered in classical multi-parameter treatments.

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“…Beran (1984), and Hinkley and Wei (1984) have discussed the jackknife estimation of the skewness. The simulation studies by Beran (1984), Schemper (1987), and Tu and Zhang (1992) show that the jackknife skewness estimators have large downward biases. Beran (1984) further has found that the biases in skewness estimators have a significant impact on the accuracy of the jackknifed Edgeworth approximation and the correctness of confidence intervals based on this approximation.…”

Section: Skewness Estimatormentioning

confidence: 95%

Asymptotic Representations of Skewness Estimators of Studentized $ U $-Statistics

Maesono¹

2004

Bulletin of Informatics and Cybernetics

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A skewness is a measure of symmetry of a distribution and appears in an Edgeworth expansion of a standardized or studentized statistic. It has been found in simulation studies that jackknife estimators of the skewness have downward biases. Fujioka and Maesono (2000) have obtained a normalizing transformation with residual term o(n −1) and they pointed out that in order to construct the normalizing transformation, we need an asymptotic representation of a skewness estimator. Maesono (1998) has obtained the asymptotic representation of the jackknife skewness estimators and discussed their biases. In this paper we propose another skewness estimator of a U-statistic and obtain asymptotic representations of both estimators with remainder term o p (n −1) and discuss the biases theoretically.

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On the estimation of skewness of a statistic using the jackknife and the bootstrap

Cited by 11 publications

References 12 publications

A conditional nonparametric analysis for measuring the efficiency of regional public healthcare delivery: An application to Greek prefectures

A conditional nonparametric analysis for measuring the efficiency of regional public healthcare delivery: An application to Greek prefectures

QUALITY PAPERA new rapid and robust multi-factorial screening for low-percentile use-rate accelerated reliability analysis

Asymptotic Representations of Skewness Estimators of Studentized $ U $-Statistics

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