Robust Estimation &amp; Testing

Staudte, Robert G.; Sheather, Simon J.

doi:10.1002/9781118165485

Cited by 431 publications

(314 citation statements)

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“…Although the Type I error rate is widely viewed as being relatively unaffected by non-normality, Bradley (1980) has pointed out conditions in which this is not true. This finding is also evident in the findings of recent studies and published texts (e. g., See Hempel, Ronchetti, & Rousseeuw, 1986;Huber & Ronchetti, 2009;Maronna, Martin, & Yohai, 2006;Micceri, 1989;Schoder, et al, 2006;Staudte & Sheather, 1990;Wilcox, 2012a, b;Wilcox & Keselman, 2003).…”

Section: Introductionsupporting

confidence: 64%

Preliminary Testing for Normality: Is This a Good Practice?

Keselman

Othman

Wilcox

2013

J. Mod. App. Stat. Meth.

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Section: Introductionsupporting

confidence: 64%

Preliminary Testing for Normality: Is This a Good Practice?

Keselman

Othman

Wilcox

2013

J. Mod. App. Stat. Meth.

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“…We consider Cushny and Peebles data which is given in Staudte and Sheather (1990). The data show the differing effects of optical isomers of hyoscyamine hydrobromide in producing sleep.…”

Section: Examplementioning

confidence: 99%

“…The data show the differing effects of optical isomers of hyoscyamine hydrobromide in producing sleep. We compare sample conceptual mean ( ) with mean and Huber's estimators which are given by Staudte and Sheather (1990) Where ̂ is Huber's estim te.…”

Section: Examplementioning

confidence: 99%

“…Using normal contamination model, Tukey (1960) dramatically demonstrated how little efficient the mean can become when contamination increases, also showed that alternative location estimators such as the median can achieve higher asymptotic efficiency than the mean. As a result, considerable effort has been put into the development of procedures for the robust estimation of measures of location where the statisticians have felt aware of the need for robust procedures, in the sense of procedures that remain good when the assumed model does not quite fit; see, for example, Staudte and Sheather (1990) and Huber (1981) for a comprehensive accounts of these developments.…”

Section: Introductionmentioning

confidence: 99%

“…Two good choices are Huber's M-estimator and Hodges-Lehmann estimator. The former minimizes ∑ when is chosen to be quadratic for small values and linear for larger one where is the location parameter; see, Huber (1981) and the latter is the median of pairwise averages ( ; see, Staudte and Sheather (1990). These estimators maintain good efficiency from small to large sample sizes for a wide range of symmetric distributions but exact variances and distribution-free of these variances are not directly available for these estimators.…”

Section: Introductionmentioning

confidence: 99%

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Extended Mean with Distribution-Free Variance

Kandil¹,

Hamza²

2015

IJBSA

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Location estimation is one of the basic activities in statistical data analysis so considerable effort has been put into the development of procedures for the robust estimation of measures of location. Because the distribution-free variance of most of existing measures is difficult to obtain in closed form, these measures work under strong modelling assumptions. We propose a robust location measure in which the expectation of a lower order statistics is replaced by the expectation of a larger order statistics. The main attraction of this measure is that its distribution-free variance is obtained in closed form. Comparisons with some of the best location estimators, mean, Hodges-Lehmann estimator, Huber's M-estimator and median are given based on Monte Carlo simulations. Computationally, the new estimator has an explicit expression and requires no iteration.

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Resistant, Robust and Non-Parametric Techniques for the Analysis of Climate Data: Theory and Examples, Including Applications to Historical Radiosonde Station Data

1996

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Basic traditional parametric statistical techniques are used widely in climatic studies for characterizing the level (central tendency) and variability of variables, assessing linear relationships (including trends), detection of climate change, quality control and assessment, identification of extreme events, etc. These techniques may involve estimation of parameters such as the mean (a measure of location), variance (a measure of scale) and correlation/regression coefficients (measures of linear association); in addition, it is often desirable to estimate the statistical significance of the difference between estimates of the mean from two different samples as well as the significance of estimated measures of association. The validity of these estimates is based on underlying assumptions that sometimes are not met by real climate data. Two of these assumptions are addressed here: normality and homogeneity (and as a special case statistical stationarity); in particular, contamination from a relatively few ‘outlying values’ may greatly distort the estimates. Sometimes these common techniques are used in order to identify outliers; ironically they may fail because of the presence of the outliers! Alternative techniques drawn from the fields of resistant, robust and non‐parametric statistics are usually much less affected by the presence of ‘outliers’ and other forms of non‐normality. Some of the theoretical basis for the alternative techniques is presented as motivation for their use and to provide quantitative measures for their performance as compared with the traditional techniques that they may replace. Although this work is by no means exhaustive, typically a couple of suitable alternatives are presented for each of the common statistical quantities/tests mentioned above. All of the technical details needed to apply these techniques are presented in an extensive appendix. With regard to the issue of homogeneity of the climate record, a powerful non‐parametric technique is introduced for the objective identification of ‘change‐points’ (discontinuities) in the mean. These may arise either naturally (abrupt climate change) or as the result of errors or changes in instruments, recording practices, data transmission, processing, etc. The change‐point test is able to identify multiple discontinuities and requires no ‘metadata’ or comparison with neighbouring stations; these are important considerations because instrumental changes are not always documented and, particularly with regard to radiosonde observations, suitable neighbouring stations for ‘buddy checks’ may not exist. However, when such auxiliary information is available it may be used as independent confirmation of the artificial nature of the discontinuities. The application and practical advantages of these alternative techniques are demonstrated using primarily actual radiosonde station data and in a few cases using some simulated (artificial) data as well. The ease with which suitable examples were obtained from the radiosonde archive begs fo...

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Robust Estimation & Testing

Cited by 431 publications

References 0 publications

Preliminary Testing for Normality: Is This a Good Practice?

Preliminary Testing for Normality: Is This a Good Practice?

Extended Mean with Distribution-Free Variance

Resistant, Robust and Non-Parametric Techniques for the Analysis of Climate Data: Theory and Examples, Including Applications to Historical Radiosonde Station Data

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