The DOI matches its Crossref record.
Low Moments for Small Samples: A Comparative Study of Order Statistics
Open accessAbstract
The means, variances, and covariances for samples of size $\leq 10$ from the normal distribution, a selected long-tailed distribution, and the uniform distribution are tabled and compared with the usual asymptotic approximations. The methods of computation used and the accuracy expected are discussed. Use is made of the representation of an arbitrarily distributed variate as a monotone function of a uniformly (rectangularly) distributed variate. It is hoped that these tables will encourage experimentation with new statistical procedures.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“For example, outliers in linear models may strongly impact linear estimators, and some studies may therefore adopt a modeling strategy wherein values are winsorized (e.g., extreme values can be truncated at the 2.5th and 97.5th quantiles56).”
From Guidelines for wrist-worn consumer wearable assessment of heart rate in biobehavioral research (2020) · cites this paper as [56]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Sorted by citations
An analysis of variance test for normality (complete samples)
SHAPIRO, S. S., & WILK, M. B. (1965) · Biometrika · doi:10.1093/biomet/52.3-4.591 · Cited by 23,480
A Comparative Study of Various Tests for Normality
Shapiro, S. S., Wilk, M. B., & Chen, H. J. (1968) · Journal of the American Statistical Association · doi:10.1080/01621459.1968.10480932 · Cited by 1,192
Metabolic Reconstruction for Metagenomic Data and Its Application to the Human Microbiome
Abubucker, S., Segata, N., Goll, J. B., Schubert, A. M., Izard, J., Cantarel, B. L., Rodriguez-Mueller, B., Zucker, J., Thiagarajan, M., Henrissat, B., et al. (2012) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002358 · Cited by 1,076
“These differences were summarized into overall patterns of variation using principal component analysis on a matrix of average module abundances per body site, Winsorized at 20% (a robust arithmetic mean [30]), filtered at a minimum of 0.01% in at least one site, and normalized to z-scores.”
MethodInfluentialComparisons of various types of normality tests
Yap, B. W., & Sim, C. H. (2011) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2010.520163 · Cited by 897
“gif"/> , originally proposed by Ramberg and Schmeiser 36 , is a four-parameter generalization of the two-parameter Tukey's Lambda family of distribution 37 and Karian and Dudewicz 38 has published tables that provide parameter <inline-graphic xmlns:xlink="http://www.”
BackgroundGenome-wide probing of RNA structure reveals active unfolding of mRNA structures in vivo
Rouskin, S., Zubradt, M., Stefan Washietl, A., Kellis, M., & Weissman, J. S. (2013) · Nature · doi:10.1038/nature12894 · Cited by 862
On unbiased estimates of the population mean based on the sample stratified by means of ordering
Takahasi, K., & Wakimoto, K. (1968) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf02911622 · Cited by 764
DIVISION OF PSYCHOLOGY : STATISTICAL FACILITATION OF SIMPLE REACTION TIMES*
Raab, D. H. (1962) · Transactions of the New York Academy of Sciences · doi:10.1111/j.2164-0947.1962.tb01433.x · Cited by 668
An approximate method for generating symmetric random variables
Ramberg, J. S., & Schmeiser, B. W. (1972) · Communications of the ACM · doi:10.1145/355606.361888 · Cited by 398
Characterizing transcriptional heterogeneity through pathway and gene set overdispersion analysis
Fan, J., Salathia, N. S., Liu, R., Kaeser, G. E., Yung, Y. C., Herman, J. L., Kaper, F., Fan, J., Zhang, K., Chun, J. J. M., et al. (2016) · Nature Methods · doi:10.1038/nmeth.3734 · Cited by 376
An approximate method for generating asymmetric random variables
Ramberg, J. S., & Schmeiser, B. W. (1974) · Communications of the ACM · doi:10.1145/360827.360840 · Cited by 353
Mills, S., Brown, H., Wrieden, W. L., White, M. J., & Adams, J. M. (2017) · International Journal of Behavioral Nutrition and Physical Activity · doi:10.1186/s12966-017-0567-y · Cited by 349
“Dietary intake values were winsorized at 1st and 99th percentiles, by replacing the smallest and largest percentage values in the distribution with the observations closest to them [30].”
MethodGuidelines for wrist-worn consumer wearable assessment of heart rate in biobehavioral research
Nelson, B. W., Low, C. A., Jacobson, N., Areán, P., Torous, J., & Allen, N. B. (2020) · npj Digital Medicine · doi:10.1038/s41746-020-0297-4 · Cited by 241
a study of the generalized tukey lambda family
Freimer, M. L., Kollia, G. D., Mudholkar, G. S., & Lin, C. T. (1988) · Communication in Statistics- Theory and Methods · doi:10.1080/03610928808829820 · Cited by 230
Methods for generating families of univariate continuous distributions in the recent decades
Lee, C., Famoye, F., & Alzaatreh, A. (2013) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.1255 · Cited by 177
“, exponentiation), (3) beta generated method, (4) transformed-transformer method, and (5) composite method.”
Lesh, T. A., Westphal, A. J., Niendam, T. A., Yoon, J. H., Minzenberg, M., Ragland, J. D., Solomon, M., & Carter, C. S. (2013) · NeuroImage Clinical · doi:10.1016/j.nicl.2013.04.010 · Cited by 193
“Consequently, a Winsorizing procedure (Dixon, 1960; Hastings et al., 1947) was applied to values exceeding the 99th percentile.”
MethodA hybrid recommender system using artificial neural networks
Paradarami, T. K., Bastian, N. D., & Wightman, J. L. (2017) · Expert Systems with Applications · doi:10.1016/j.eswa.2017.04.046 · Cited by 164
Some Properties of the Range in Samples from Tukey's Symmetric Lambda Distributions
Joiner, B. L., & Rosenblatt, J. R. (1971) · Journal of the American Statistical Association · doi:10.1080/01621459.1971.10482275 · Cited by 151
“[6] and Filliben [2].”
MethodSoil microbiome signatures are associated with pesticide residues in arable landscapes
Walder, F., Schmid, M. W., Riedo, J., Valzano‐Held, A., Banerjee, S., Büchi, L., Bucheli, T. D., & van der Heijden, M. G. A. (2022) · Soil Biology and Biochemistry · doi:10.1016/j.soilbio.2022.108830 · Cited by 152
Tukey, J. W., & McLaughlin, D. H. (2016) · Cited by 127
Self-citationRobust Estimation via Robust Gradient Estimation
Prasad, A., Suggala, A. S., Balakrishnan, S., & Ravikumar, P. (2020) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12364 · Cited by 128
“However, a major drawback with this classical line of work has been that most of the estimators with strong robustness guarantees are computationally intractable [2], while the remaining ones use heuristics and are consequently not optimal [21].”
BackgroundWei, M. Y., & Mukamal, K. J. (2017) · American Journal of Epidemiology · doi:10.1093/aje/kwx198 · Cited by 111
ON THE MOMENTS OF ORDER STATISTICS IN SAMPLES FROM NORMAL POPULATIONS
Ruben, H. (1954) · Biometrika · doi:10.1093/biomet/41.1-2.200 · Cited by 112
Nielsen, A. B., Thorsen‐Meyer, H., Belling, K., Nielsen, A. P., Thomas, C. E., Chmura, P. J., Lademann, M., Moseley, P. L., Heimann, M., Dybdahl, L., et al. (2019) · The Lancet Digital Health · doi:10.1016/s2589-7500(19)30024-x · Cited by 109
“We used a combination of Tukey’s and Winsor’s methods 18,19 to normalise data for the continuous variables.”
MethodGfrerer, L., Mattos, D., Mastroianni, M., Weng, Q. Y., Ricci, J. A., Heath, M. P., Lin, A. M., Specht, M. C., Haynes, A. B., Austen, W. G., et al. (2015) · Plastic & Reconstructive Surgery · doi:10.1097/prs.0000000000000912 · Cited by 101
Pollet, T., & van der Meij, L. (2016) · Adaptive Human Behavior and Physiology · doi:10.1007/s40750-016-0050-z · Cited by 94
Robust measures of tail weight
Brys, G., Hubert, M., & Struyf, A. (2004) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2004.09.012 · Cited by 95
“Note that the Tukey Lambda distribution [12] with parameter λ (say TL(λ)) is defined as: Y = X λ−(1−X)λ λ λ 6= 0 Y = Logistic λ = 0 with X ∼ Uniform(0, 1).”
Workload modeling for resource usage analysis and simulation in cloud computing
Magalhães, D. M. V., Calheiros, R. N., Buyya, R., & Gomes, D. G. (2015) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2015.08.016 · Cited by 93
A New Extension of Generalized Exponential Distribution with Application to Ozone Data
Dey, S., Alzaatreh, A., Zhang, C., et al. (2017) · Ozone Science and Engineering · doi:10.1080/01919512.2017.1308817 · Cited by 92
Wilks, S. S. (1948) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1948-08936-4 · Cited by 95
Spot and forward volatility in foreign exchange
Corte, P. D., Sarno, L., & Tsiakas, I. (2011) · Journal of Financial Economics · doi:10.1016/j.jfineco.2011.01.007 · Cited by 90
The Swiss Household Panel Study: Observing social change since 1999
Tillmann, R., Voorpostel, M., Antal, E., Kuhn, U., Lebert, F., Ryser, V.-A., Lipps, O., & Wernli, B. (2016) · Longitudinal and Life Course Studies · doi:10.14301/llcs.v7i1.360 · Cited by 85
On Moments of Order Statistics and Quasi-ranges from Normal Populations
Govindarajulu, Z. (1963) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177704176 · Cited by 80
Fractional Order Statistics, with Applications
Stigler, S. M. (1977) · Journal of the American Statistical Association · doi:10.1080/01621459.1977.10480611 · Cited by 78
Validity of the Exercise Vital Sign Tool to Assess Physical Activity
Kuntz, J. L., Young, D. R., Saelens, B. E., Frank, L. D., Meenan, R. T., Dickerson, J. F., Keast, E. M., & Fortmann, S. P. (2021) · American Journal of Preventive Medicine · doi:10.1016/j.amepre.2021.01.012 · Cited by 79
Numerical maximum log likelihood estimation for generalized lambda distributions
Su, S. Y. S. (2006) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2006.06.008 · Cited by 76
Patil, G. P., Sinha, A. K., & Taillie, C. (1994) · Handbook of statistics · doi:10.1016/s0169-7161(05)80007-0 · Cited by 75
Oxygen consumption and distribution in the Long-Evans rat retina
Lau, J. C., & Linsenmeier, R. A. (2012) · Experimental Eye Research · doi:10.1016/j.exer.2012.07.004 · Cited by 74
“The data sets for these parameters were Winsorized at the 10th percentile (Barnett and Lewis, 1978; Hastings et al., 1947) to minimize the aberrant influence of the outlier.”
A New Extension of Weibull Distribution with Application to Lifetime Data
Dey, S., Sharma, V. K., & Mesfioui, M. (2017) · Annals of Data Science · doi:10.1007/s40745-016-0094-8 · Cited by 72
Bernard, R. M., Borokhovski, E., Schmid, R. F., Waddington, D. I., & Pickup, D. I. (2019) · Campbell Systematic Reviews · doi:10.1002/cl2.1017 · Cited by 110
Karas, M., Muschelli, J., Leroux, A., Urbanek, J. K., Wanigatunga, A. A., Bai, J., Crainiceanu, C. M., & Schrack, J. A. (2022) · JMIR mhealth and uhealth · doi:10.2196/38077 · Cited by 71
“Activity count, monitor-independent movement summary, Euclidean norm minus one, mean amplitude deviation, and activity intensity data were winsorized [18] to reduce the effect of extreme values in the data set, by computing the measure-specific 0.”
MethodMultimorbidity and Mental Health‐Related Quality of Life and Risk of Completed Suicide
Wei, M. Y., & Mukamal, K. J. (2018) · Journal of the American Geriatrics Society · doi:10.1111/jgs.15678 · Cited by 67
“To assess for a potential nonlinear association between MWI and suicide mortality, we used restricted cubic splines(31) and winsorized the top 5% MWI values to reduce the possible effect of spurious outliers.(32) Nonlinearity was tested through the likelihood ratio test to compare models with one linear term vs both l…”
MethodJensen, P. N., Fretts, A. M., Yu, C., Hoofnagle, A. N., Umans, J. G., Howard, B. V., Sitlani, C. M., Siscovick, D. S., King, I. B., Sotoodehnia, N., et al. (2018) · EBioMedicine · doi:10.1016/j.ebiom.2018.12.046 · Cited by 63
“Due to potential high influence of very large values, fasting glucose levels at follow-up exceeding 200 mg/dL (n = 36; 98th percentile) were Winsorized at 200mg/dL [12].”
BackgroundReinventing a business model in industrial networks: Implications for customers' brand perceptions
Spieth, P., Röth, T., & Meissner, S. (2019) · Industrial Marketing Management · doi:10.1016/j.indmarman.2019.04.013 · Cited by 61
A BIBLIOGRAPHY ON LIFE TESTING AND RELATED TOPICS
Mendenhall, W. M. (1958) · Biometrika · doi:10.1093/biomet/45.3-4.521 · Cited by 58
Relationships between electrochemical skin conductance and kidney disease in Type 2 diabetes
Freedman, B. I., Bowden, D. W., Smith, S. C., et al. (2013) · Journal of Diabetes and its Complications · doi:10.1016/j.jdiacomp.2013.09.006 · Cited by 53
Some Low Moments of Order Statistics
Godwin, H. J. (1949) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177730036 · Cited by 54
Exploratory Shopping: Attention Affects In-Store Exploration and Unplanned Purchasing
Streicher, M. C., Estes, Z., & Büttner, O. B. (2020) · Journal of Consumer Research · doi:10.1093/jcr/ucaa054 · Cited by 42
A Second-Order Method for Assembly Tolerance Analysis
Glancy, C. G., & Chase, K. W. (1999) · doi:10.1115/detc99/dac-8707 · Cited by 53
Birnbaum, A., & Dudman, J. (1963) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177704178 · Cited by 52
Apolipoprotein L1 & Chronic Kidney Disease Risk in Young Potential Living Kidney Donors
Locke, J., Sawinski, D., Reed, R., Shelton, B. A., MacLennan, P., Kumar, V., Mehta, S., Mannon, R., Gaston, R., Julian, B., et al. (2017) · Annals of Surgery · doi:10.1097/sla.0000000000002174 · Cited by 49
The Swiss Household Panel (SHP)
Tillmann, R., Voorpostel, M., Antal, E., et al. (2021) · Jahrbücher für Nationalökonomie und Statistik · doi:10.1515/jbnst-2021-0039 · Cited by 50
“In rare cases, Winsorisation (Hastings et al. 1947) is needed to correct for negative or extreme weights.”
BackgroundA preliminary study of an online psychoeducational program for hypersexuality
Hardy, S. A., Ruchty, J., Hull, T. D., & Hyde, R. (2010) · Sexual Addiction & Compulsivity · doi:10.1080/10720162.2010.533999 · Cited by 49
“Rather than omit these cases, the values were Winsorized ( Hasings, Mosteller, Tukey, & Winsor, 1947 ), which entails recoding them to the highest non-outlier value.”
BackgroundCostello-White, R., Ryff, C. D., & Coe, C. L. (2015) · AGE · doi:10.1007/s11357-015-9808-7 · Cited by 48
“To limit the influence of outlier values, a small number of extremely high values outside the third standard deviation of the distribution were removed before all values were log transformed following the statistical recommendations of Tukey and Winsor (Hasings et al. 1947).”
MethodZampieri, F. G., Ranzani, O., Azevedo, L. C. P., Martins, I. D. S., Kellum, J. A., & Libório, A. B. (2016) · Critical Care Medicine · doi:10.1097/ccm.0000000000001948 · Cited by 51
“For continuous variables, outliers were winsorized at percentiles 1 and 99 (34).”
MethodRobust solutions and risk measures for a supply chain planning problem under uncertainty
Poojari, C. A., Lucas, C. A., & Mitra, G. (2007) · Journal of the Operational Research Society · doi:10.1057/palgrave.jors.2602381 · Cited by 46
“The GLD (Ramberg and Schmeiser, 1974) is a four parameter generalization of Tukey’s Lambda family (Hastings et al, 1947), that has proved useful in a number of different applications.”
BackgroundMethodDurbin–Watson and Generalized Durbin–Watson Tests for Autocorrelations and Randomness
Ali, M. M. (1987) · Journal of Business and Economic Statistics · doi:10.1080/07350015.1987.10509578 · Cited by 46
Su, S. Y. S. (2007) · Journal of Statistical Software · doi:10.18637/jss.v021.i09 · Cited by 46
MOMENTS OF ORDER STATISTICS FROM A NORMAL POPULATION
Bose, R. C., & Gupta, S. S. (1959) · Biometrika · doi:10.1093/biomet/46.3-4.433 · Cited by 45
Characterizing the effects of feature salience and top-down attention in the early visual system
Poltoratski, S., Ling, S., McCormack, D. R., & Tong, F. (2017) · Journal of Neurophysiology · doi:10.1152/jn.00924.2016 · Cited by 45
“Outliers were defined as time points for which the voxel’s response measured more than three times its standard deviation from its mean and were Winsorized (Hastings et al. 1947).”
BackgroundSkewness-Invariant Measures of Kurtosis
Jones, M. C., Rosco, J. F., & Pewsey, A. (2011) · The American Statistician · doi:10.1198/tast.2011.10194 · Cited by 44
“That one is the celebrated Tukey lambda distribution (Hastings et al. 1947; Tukey 1962) which has quantile function Q (u) = λ−1{ u − (1 − u)λ}.”
BackgroundBiagianti, B., Roach, B. J., Fisher, M., Loewy, R. L., Ford, J. M., Vinogradov, S., & Mathalon, D. H. (2017) · Neuropsychiatric Electrophysiology · doi:10.1186/s40810-017-0024-9 · Cited by 43
“Cognitive variables were screened and normally distributed after winsorising of outlying values [86].”
BackgroundRobustness to nonnormality of regression F-tests
Ali, M. M., & Sharma, S. C. (1996) · Journal of Econometrics · doi:10.1016/0304-4076(94)01700-x · Cited by 45
Interpretable boosting tree ensemble method for multisource building fire loss prediction
Wang, N., Xu, Y. Q., & Wang, S. (2022) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2022.108587 · Cited by 41
Eclipse: An End-to-End Platform for Low-Cost, Hyperlocal Environmental Sensing in Cities
Daepp, M. I. G., Cabral, A., Ranganathan, V. N., Iyer, V., Counts, S., Johns, P., Roseway, A., Catlett, C., Jancke, G., Gehring, D., et al. (2022) · ACM/IEEE International Conference on Information Processing in Sensor Networks (IPSN) · doi:10.1109/ipsn54338.2022.00010 · Cited by 40
“1% of readings were trimmed to improve robustness to outliers) [28] and PM2.”
BackgroundMoqtaderi, Z., Geisberg, J. V., & Struhl, K. (2018) · Molecular Cell · doi:10.1016/j.molcel.2018.08.044 · Cited by 35
Poltoratski, S., Maier, A., Newton, A. T., & Tong, F. (2019) · Current Biology · doi:10.1016/j.cub.2019.04.068 · Cited by 40
Modelling exchange rate returns: which flexible distribution to use?
Corlu, C. G., & Corlu, A. (2014) · Quantitative Finance · doi:10.1080/14697688.2014.942231 · Cited by 38
“The GLD (Joiner and Rosenblatt 1971, Ramberg and Schmeiser 1974, Filliben 1975), which is an extension of Tukey’s lambda distribution (Hastings et al. 1947) is defined by the following inverse cumulative distribution function (cdf): F−1(u; λ1, λ2, λ3, λ4) = λ1 + u λ3 − (1 − u)λ4 λ2 (1) where 0 ≤ u…”
BackgroundEstimates of Parameters of a Censored Regression Sample
Chen, E. H., & Dixon, W. J. (1972) · Journal of the American Statistical Association · doi:10.1080/01621459.1972.10481273 · Cited by 38
“Important contributions to this subject include [9, 13, 15, 10, 21].”
Spatially aware clustering of ion images in mass spectrometry imaging data using deep learning
Zhang, W., Claesen, M., Moerman, T., Groseclose, M. R., Waelkens, E., Moor, B. D., & Verbeeck, N. (2021) · Analytical and Bioanalytical Chemistry · doi:10.1007/s00216-021-03179-w · Cited by 40
Dube, F., Nzimande, N. P., & Muzindutsi, P. (2021) · Journal of Sustainable Finance & Investment · doi:10.1080/20430795.2021.2017257 · Cited by 37
Cohen, A., Sarhan, A. E., & Greenberg, B. (1958) · Mathematical Tables and Other Aids to Computation · doi:10.2307/2002387 · Cited by 37
DOES FINANCIAL INCLUSION DRIVE THE ISLAMIC BANKING EFFICIENCY? A POST-FINANCIAL CRISIS ANALYSIS
Banna, H., Alam, M. R., Ahmad, R. B., & Sari, N. M. (2020) · The Singapore Economic Review · doi:10.1142/s0217590819420050 · Cited by 38
Verburg, E., van Gils, C. H., Bakker, M. F., et al. (2020) · Investigative Radiology · doi:10.1097/rli.0000000000000656 · Cited by 36
“Before model fitting, feature values labeled as outliers in the training set were censored by clipping the extreme values.(26) To prevent overfitting, model weights were reduced for each fit using Ridge regression.”
MethodAn Introduction to Machine Learning for Panel Data
Chen, J. M. (2021) · International Advances in Economic Research · doi:10.1007/s11294-021-09815-6 · Cited by 34
Zimmerman, J. E., Chan, M. T., Jackson, N., Maislin, G., & Pack, A. I. (2012) · SLEEP · doi:10.5665/sleep.1744 · Cited by 38
Lau, J. C., Kroes, R. A., Moskal, J. R., & Linsenmeier, R. A. (2013) · Europe PMC (PubMed Central) · Cited by 38
Bornheimer, L. A. (2016) · Schizophrenia Research · doi:10.1016/j.schres.2016.07.009 · Cited by 40
Some consequences of applying lognormal theory to pseudolognormal distributions
Link, R. F., & Koch, G. S. (1975) · Mathematical Geology · doi:10.1007/bf02080488 · Cited by 35
Precipitous Dehydroepiandrosterone Declines Reflect Decreased Physical Vitality and Function
Rendina, D. N., Ryff, C. D., & Coe, C. L. (2016) · The Journals of Gerontology Series A · doi:10.1093/gerona/glw135 · Cited by 34
Thaler, N. S., Hill, B. D., Duff, K. M., Mold, J. W., & Scott, J. G. (2015) · Journal of Clinical and Experimental Neuropsychology · doi:10.1080/13803395.2015.1039962 · Cited by 34
Cortisol reactions to a social evaluative paradigm in 5- and 6-year-old children
de Weerth, C., Zijlmans, M. A. C., Mack, S., & Beijers, R. (2012) · Stress · doi:10.3109/10253890.2012.684112 · Cited by 32
“This outlier was replaced by the variable mean plus three times its standard deviation (Hasings et al., 1947).”
MethodProbability aggregation in time-series: Dynamic hierarchical modeling of sparse expert beliefs
Satopaa, V., Jensen, S. T., Mellers, B., Tetlock, P., & Ungar, L. (2014) · The Annals of Applied Statistics · doi:10.1214/14-aoas739 · Cited by 30
“This is similar to winsorising that sets the extreme probabilities to a specified percentile of the data [see, e.g., Hastings et al. (1947) for more details on winsorising].”
BackgroundRobustness to nonnormality of the Durbin-Watson test for autocorrelation
Ali, M. M., & Sharma, S. C. (1993) · Journal of Econometrics · doi:10.1016/0304-4076(93)90061-9 · Cited by 32
Optimal Robustness: A General Method, with Applications to Linear Estimators of Location
Birnbaum, A., & LASKA, E. M. (1967) · Journal of the American Statistical Association · doi:10.1080/01621459.1967.10500928 · Cited by 32
Divorce/Separation in Later-Life: A Fixed Effects Analysis of Economic Well-Being by Gender
Sharma, A. (2014) · Journal of Family and Economic Issues · doi:10.1007/s10834-014-9432-1
“Although trimming 1 % of the sample is one possibility, a more appropriate approach for this analysis is to Winsor the data, thereby retaining the small sample size for the D/S category and maintaining statistical power (Hastings et al. 1947; Tukey 1962; Salkind 2010).”
MethodA Uniformly Asymptotically Efficient Estimator of a Location Parameter
Takeuchi, K. (1971) · Journal of the American Statistical Association · doi:10.1080/01621459.1971.10482258 · Cited by 31
Evaluating English language learners’ conversations: Man vs. Machine
Forsyth, C. M., Luce, C., Zapata‐Rivera, D., Jackson, G. T., Evanini, K., & So, Y. (2018) · Computer Assisted Language Learning · doi:10.1080/09588221.2018.1517126 · Cited by 33
“Outliers within the data were replaced via the Winsor method (Hastings, Mosteller, Tukey, & Winsor, 1947).”
MethodYu, C., Zou, Z., Shao, Y., et al. (2019) · Kybernetes · doi:10.1108/k-04-2019-0223 · Cited by 30
Murea, M., Register, T. C., Divers, J., Bowden, D. W., Carr, J. J., Hightower, C. R., Xu, J., Smith, S. C., Hruska, K. A., Langefeld, C. D., et al. (2012) · BMC Nephrology · doi:10.1186/1471-2369-13-148 · Cited by 28
“7 [28].”
Learner Groups in Massive Open Online Courses
Arora, S., Goel, M., Sabitha, A. S., et al. (2017) · American Journal of Distance Education · doi:10.1080/08923647.2017.1300461 · Cited by 28
“This technique of outlier treatment is called Winsorization or Percentile Capping — substituting extreme values with less extreme values (Hastings et al. 1947).”
MethodPoltoratski, S., & Tong, F. (2020) · Journal of Neuroscience · doi:10.1523/jneurosci.2377-19.2020 · Cited by 26
“Outliers were defined as time points for which the voxel’s response measured more than 3 times its standard deviation from its mean, and were Winsorised (Hastings et al., 1947).”
BackgroundGalbraith, A. A., Meyers, D. J., Ross‐Degnan, D., Burns, M. E., Vialle-Valentin, C. E., Larochelle, M. R., Touw, S., Zhang, F., Rosenthal, M. B., & Balaban, R. B. (2017) · Health Services Research · doi:10.1111/1475-6773.12790 · Cited by 27
Empirical distributions of daily equity index returns: A comparison
Corlu, C. G., Meterelliyoz, M., & Tiniç, M. (2016) · Expert Systems with Applications · doi:10.1016/j.eswa.2015.12.048 · Cited by 26
Kafadar, K. (2003) · Statistical Science · doi:10.1214/ss/1076102419 · Cited by 26
Extended Models for Quantal Response Data
Morgan, B. J. T. (1988) · Statistica Neerlandica · doi:10.1111/j.1467-9574.1988.tb01239.x · Cited by 26
Mehrotra, R., Stanaway, I. B., Jarvik, G. P., Lambie, M., Morelle, J., Perl, J. M., Himmelfarb, J., Heimbürger, O., Johnson, D. W., Imam, T. H., et al. (2021) · Kidney International · doi:10.1016/j.kint.2021.05.037 · Cited by 26
A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data
Su, S. Y. S. (2005) · Journal of Modern Applied Statistical Methods · doi:10.22237/jmasm/1130803560 · Cited by 25
ciRS-7 and miR-7 regulate ischemia-induced neuronal death via glutamatergic signaling
Scoyni, F., Sitnikova, V., Giudice, L., Korhonen, P., Trevisan, D. M., Hernandez de Sande, A., Gomez-Budia, M., Giniatullina, R., Ugidos, I. F., Dhungana, H., et al. (2024) · Cell Reports · doi:10.1016/j.celrep.2024.113862 · Cited by 27
Deimling, G. T., Pappada, H. T. R., Ye, M., Nalepa, E., Ciaralli, S. R., Phelps, E. K., & Burant, C. J. (2017) · Journal of Aging and Health · doi:10.1177/0898264317745745 · Cited by 24
Poorer sleep impairs brain health at midlife
Namsrai, T., Ambikairajah, A., & Cherbuin, N. (2023) · Scientific Reports · doi:10.1038/s41598-023-27913-9 · Cited by 26
Metadata
- Authors
- Hastings, C., Mosteller, F., Tukey, J. W., & Winsor, C. P.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1947-09
- Volume
- 18
- Issue
- 3
- Pages
- 413-426
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2040509998
- Cited by
- 366
- References
- 0
- Citations by year
- 2026: 18 · 2025: 10 · 2024: 10 · 2023: 14 · 2022: 18 · 2021: 27 · 2020: 24 · 2019: 22 · 2018: 18 · 2017: 26 · 2016: 17 · 2015: 17 · 2014: 14 · 2013: 14 · 2012: 14
- FWCI
- 6.85
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Mathematical Statistics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- order statistics, moments, normal distribution, long-tailed distributions, uniform distribution, asymptotic approximation, mathematical tables
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
