Two Nonparametric Predictive Control Charts

Arts, G.R.J.; Coolen, Frank P. A.

doi:10.1080/15598608.2008.10411890

Cited by 10 publications

(9 citation statements)

References 16 publications

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“…In addition to the scenarios used in this article, NPI has, for example, been presented for multinomial data and lifetime data with right-censored observations (Coolen 2011). Recently presented NPI methods for statistical inference and decision support considered, for example, quality control (Arts et al 2004;Arts and Coolen 2008), precedence testing (Coolen-Schrijner et al 2009), accuracy of diagnostic tests (Coolen-Maturi et al 2012;Elkhafifi and Coolen 2012), and acceptance decisions (Coolen and Elsaeiti 2009;Elsaeiti and Coolen 2012).…”

Section: Nonparametric Predictive Inference For the Reproducibility Pmentioning

confidence: 99%

Nonparametric Predictive Inference for Reproducibility of Basic Nonparametric Tests

Coolen

Himd

2014

Journal of Statistical Theory and Practice

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Reproducibility of tests is an important characteristic of the practical relevance of test outcomes. Recently, there has been substantial interest in the reproducibility probability (RP), where not only its estimation but also its actual definition and interpretation are not uniquely determined in the classical frequentist statistics framework. Nonparametric predictive inference (NPI) is a frequentist statistics approach that makes few assumptions, enabled by the use of lower and upper probabilities to quantify uncertainty, and that explicitly focuses on future observations. The explicitly predictive nature of NPI provides a natural formulation for inferences on RP. In this article, we introduce the NPI approach to RP for some basic nonparametric tests.

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Section: Nonparametric Predictive Inference For the Reproducibility Pmentioning

confidence: 99%

Nonparametric Predictive Inference for Reproducibility of Basic Nonparametric Tests

Coolen

Himd

2014

Journal of Statistical Theory and Practice

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“…For real-valued random quantities attention has thus far been mostly restricted to a single future observation, although multiple future observations have been considered for some NPI methods, e.g. in statistical process control [2,3].…”

Section: Nonparametric Predictive Inferencementioning

confidence: 99%

“…Assume that we have real-valued ordered data x (1) < x (2) < ⋯ < x (n) , with n ≥ 1 . For ease of notation, define x (0) = −∞ and x (n+1) = ∞ , or define these equal to other known lower and upper bounds of the range of possible values for these random quantities.…”

Section: Nonparametric Predictive Inferencementioning

confidence: 99%

“…For r = 1 and j ≥ 3 , the probability for the event X (1) ∈ I j does not break down, whereas for j = 1 , * 0.05 (P(X (1) ∈ I 1 ), (x, y 9 , y 10 , y 11 )) = 3 11 = 0.2727 and for j = 2 , * 0.05 (P(X (1) ∈ I 2 ), (x, y 9 , … , y 13 )) = 5 13 = 0.3846 . These tables present the absolute value of the NPI-SC for X (2) ∈ I j , where for j = 3, 4, 5 the NPI-BP is 4 12 = 0.3333 , for j = 2 it is 5 13 = 0.3846 and for j = 6 it is 6 14 = 0.4286 . The probability for the event X (2) ∈ I j for j = 1, 7, 8, 9 , does not break down as SC P(X (2)…”

Section: Examplementioning

confidence: 99%

“…These tables present the absolute value of the NPI-SC for X (2) ∈ I j , where for j = 3, 4, 5 the NPI-BP is 4 12 = 0.3333 , for j = 2 it is 5 13 = 0.3846 and for j = 6 it is 6 14 = 0.4286 . The probability for the event X (2) ∈ I j for j = 1, 7, 8, 9 , does not break down as SC P(X (2)…”

Section: Examplementioning

confidence: 99%

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Robustness of Nonparametric Predictive Inference for Future Order Statistics

Alqifari

Coolen

2018

J Stat Theory Pract

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This paper considers robustness of Nonparametric Predictive Inference (NPI), in particular considering inference involving future order statistics. The concept of robust inference is usually aimed at development of inference methods which are not too sensitive to data contamination or to deviations from model assumptions. In this paper we use it in a slightly narrower sense. For our aims, robustness indicates insensitivity to small change in the data, as our predictive probabilities for order statistics and statistical inferences involving future observations depend upon the given observations. We introduce some concepts for assessing the robustness of statistical procedures to the NPI framework, namely sensitivity curve and breakdown point; these classical concepts require some adoption for application in NPI. Most of our nonparametric inferences have a reasonably good robustness with regard to small changes in the data.

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2014

Introduction to Imprecise Probabilities

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Two Nonparametric Predictive Control Charts

Cited by 10 publications

References 16 publications

Nonparametric Predictive Inference for Reproducibility of Basic Nonparametric Tests

Nonparametric Predictive Inference for Reproducibility of Basic Nonparametric Tests

Robustness of Nonparametric Predictive Inference for Future Order Statistics

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