The Total Median and Its Uncertainty

Cox, M G; Igúzquiza, Eulogio Pardo

doi:10.1142/9789812811684_0012

Cited by 7 publications

(7 citation statements)

References 6 publications

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“…Related work may be found in Reference [10], who give an application of the total median in metrology, in the area of intra-laboratory comparisons, providing a robust estimate of a reference value, which enables the comparison of different laboratories' nominal measures of the same quantity.…”

Section: Results and Commentsmentioning

confidence: 99%

The total median in statistical quality control

Figueiredo

Gomes

2004

Appl Stoch Models Bus & Ind

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SUMMARYIn industry, most of the process observations are assumed to come from a normal population, but usually we merely want to control the process mean value. It is thus sensible to find control statistics, which are 'robust' to monitor the process mean, giving the expected rate of false alarms whenever that mean is close to the target value, although not under a normal regime. Simulation studies for a few symmetric and asymmetric distributions allow us to suggest the total median as a robust median estimator. We shall here analyse such a robustness, as well as the robustness of the total median chart comparatively to the sample mean chart, whenever we want to control the mean value of a symmetric underlying parent. Some indication is also provided on the comparative out-of-control behaviour of the two charts.

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Section: Results and Commentsmentioning

confidence: 99%

The total median in statistical quality control

Figueiredo

Gomes

2004

Appl Stoch Models Bus & Ind

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“…This new estimator was introduced by [4] as an estimator of location and it has been extended here as an estimator of scale. The TBM is a robust and efficient estimator of the mathematical expectation and gives more weight to values around the median and less weight to the order statistics at the extremes.…”

Section: Discussionmentioning

confidence: 99%

“…Equations (23)-(26) are explicit expressions of the bootstrap mean and variance of the TBM but, by substituting the relevant weights, they are general for any L-estimator. Alternatively, the standard error of the TBM could be computed by Monte Carlo bootstrapping, as in [4], or by the asymptotic variance of the corresponding influence function as shown in the following section.…”

Section: The Tbm As An L-estimatormentioning

confidence: 99%

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The total bootstrap median: a robust and efficient estimator of location and scale for small samples

Dowd

Pardo‐Igúzquiza

Egozcue

2015

Journal of Applied Statistics

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We propose the total bootstrap median (TBM) as a robust and efficient estimator of location and scale for small samples. We demonstrate its performance by estimating the mean and variance of a variety of distributions. We also show that, if the underlying distribution is unknown and there is either no contamination or low to moderate contamination, the TBM provides a better estimate of the mean, in mean square terms, than the sample mean or the sample median. In addition, the TBM is a better estimator of the variance of the underlying distribution than the sample variance or the square of the bias-corrected median absolute deviation from the median estimator. We also show that the TBM is an explicit L-estimator, which allows a direct study of its properties.

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“…Note that these probabilities are independent of the underlying distribution F and they depend only on the sample size n. Details to obtain the a i,j,n can be found in Cox and Iguzquiza (2001) and Figueiredo and Gomes (2004). By definition, given in Equation (1), the total median statistic, TMd, is a linear combination of all the possible values of the BMd, where the weights are the previous probabilities a i,j,n , and after simple calculations it can be written as a linear combination of the sample order statistics.…”

Section: The Total Median Statisticmentioning

confidence: 99%

The total median statistic to monitor contaminated normal data

Figueiredo

Gomes

2016

Quality Technology & Quantitative Management

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Despite the advantages of the use of the normal distribution in Statistical Quality Control, the normality assumption is too restrictive for modelling real data sets, which usually exhibit asymmetry or tails heavier than the normal tails. But even in potential normal situations, there is often a small to moderate percentage of contamination in the data. In this paper, we analyze the efficiency and robustness of the total median statistic in comparison with the sample mean and the sample median to estimate the mean value of symmetric contaminated normal distributions, close to the normal, but with heavier-than-normal tails. We also compare the performance of the total median and the sample mean charts to monitor the mean value of such processes. The simulation results lead us to suggest the use of the total median statistic due to its efficiency and degree of robustness. ARTICLE HISTORY

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The Total Median and Its Uncertainty

Cited by 7 publications

References 6 publications

The total median in statistical quality control

The total median in statistical quality control

The total bootstrap median: a robust and efficient estimator of location and scale for small samples

The total median statistic to monitor contaminated normal data

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