Journal of Statisticians: Statistics and Actuarial Sciences
Research Article
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Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal

Year 2010, Volume 3, Issue 1, 8 - 16, 30.06.2010

A. F. ÖZDEMİR

Abstract

In this study, two conventional (mean and median) and three robust (trimmed mean, one-step M-estimator and modified one-step M-estimator) measures of location are compared in terms of their asymptotic relative efficiencies and mean squared error when the underlying distribution is contaminated normal.

Keywords

Contaminated normal distribution, trimmed mean, one-step M-estimator, modified one-step M-estimator, asymptotic relative efficiency

References

  • D.F. Andrews, P.J. Bickel, F.R. Hampel, P.J. Huber, W.H. Rogers, and J.W. Tukey, (1972), Robust Estimates of Location: Survey and Advaces, Princeton University Press.
  • H. Cramer, (1946), Mathematical Methods of Statistics, Princeton University Pres.
  • F.R. Hampel, (1973), Robust Estimation: A condensed partial survey. Z. Wahrscheinlichkeitstheorie Verw, Gebiete 27, 87-104.
  • M. Hill, and W.J. Dixon, (1982), Robustness in real life: A study of clinical laboratory data. Biometrics 38, 377-396.
  • P.J. Huber, (1981), Robust Statistics. Newyork: Wiley.
  • T. Micceri, (1989), The unicorn, the normal curve and other improbable creatures. Psychological Bulletin 105, 156-166.
  • R.J. Serfling, (1980), Approximation Theorems of Mathematical Statistics. Newyork: Wiley.
  • R.G. Staudte., and S.J. Sheater, (1990), Robust Estimation and Testing. Newyork: Wiley.
  • S.M. Stigler, (1973), Simon Newcomb, Percy Daniel and the history of robust estimation 1885-1920. Journal of the American Statistical Association 68, 871-879.
  • S.M. Stigler, (1977), Do robust estimators work with real data. Annals of Statistics 5, 1055-1098.
  • J.W. Tukey, (1960), A survey of sampling from contaminated normal distributions. In I.Olkin et al. (Eds), Contributions to Probability and Statistics. Stanford, CA: Stanford University
  • R.R. Wilcox, (1990), Comparing the means of two independent groups. Biometrical Journal 32, 771-780.
  • R.R. Wilcox, (2001), Fundamentals of Modern Statistical Methods. Springer-Verlag.
  • R.R. Wilcox, (2003), Modern Robust Data Analysis Methods: Measures of Central Tendency. Psychological Methods 8, 254-274.
  • R.R. Wilcox, (2005), Introduction to Robust Estimation and Hypothesis Testing. Elsevier Academic Pres, Second Edition.

Normal Dağılımdan Daha Ağır Kuyruklara Sahip Dağılımlarda Konum Ölçülerinin Karşılaştırılması

Year 2010, Volume 3, Issue 1, 8 - 16, 30.06.2010

A. F. ÖZDEMİR

Abstract

Aritmetik ortalamanın ağır kuyruklu dağılımlardan çok etkilenen bir konum ölçüsü olduğu iyi bilinen bir gerçektir. Ağır kuyruklu dağılımlar, normal dağılıma göre daha fazla aykırı değer üretme eğilimindedirler. Tukey’in belirttiği ve konu ile ilgili yapılan birçok araştırmada desteklendiği gibi uygulamada ağır kuyruklu dağılımlarla sık karşılaşılır ve bu nedenle çalışılan kitlenin ağır kuyruklu olmasının sonuçlarının anlaşılması çok yararlıdır[16, 3,  6, 11, 12, 14]. Ağır kuyruklu dağılımlar ailesinin en çok karşılaşılan üyelerinden biri bozulmuş normal dağılımdır. Bu çalışmada iki geleneksel ( aritmetik ortalama ve ortanca) ve üç dayanıklı ( budanmış ortalama ve tek-adım M-tahmincisi, düzeltilmiş tek-adım M-tahmincisi) konum ölçüsü, bozulmuş normal dağılım’dan türetilen veriler kullanılarak Asimptotik Göreli Etkinlik ve Hata Kareler Ortalaması bakımından karşılaştırılmıştır.

Keywords

Bozulmuş Normal Dağılım, budanmış ortalama, tek-adım M-tahmincisi, düzeltilmiş tek-adım M-tahmincisi, Asimptotik Göreceli Etkinlik

References

  • D.F. Andrews, P.J. Bickel, F.R. Hampel, P.J. Huber, W.H. Rogers, and J.W. Tukey, (1972), Robust Estimates of Location: Survey and Advaces, Princeton University Press.
  • H. Cramer, (1946), Mathematical Methods of Statistics, Princeton University Pres.
  • F.R. Hampel, (1973), Robust Estimation: A condensed partial survey. Z. Wahrscheinlichkeitstheorie Verw, Gebiete 27, 87-104.
  • M. Hill, and W.J. Dixon, (1982), Robustness in real life: A study of clinical laboratory data. Biometrics 38, 377-396.
  • P.J. Huber, (1981), Robust Statistics. Newyork: Wiley.
  • T. Micceri, (1989), The unicorn, the normal curve and other improbable creatures. Psychological Bulletin 105, 156-166.
  • R.J. Serfling, (1980), Approximation Theorems of Mathematical Statistics. Newyork: Wiley.
  • R.G. Staudte., and S.J. Sheater, (1990), Robust Estimation and Testing. Newyork: Wiley.
  • S.M. Stigler, (1973), Simon Newcomb, Percy Daniel and the history of robust estimation 1885-1920. Journal of the American Statistical Association 68, 871-879.
  • S.M. Stigler, (1977), Do robust estimators work with real data. Annals of Statistics 5, 1055-1098.
  • J.W. Tukey, (1960), A survey of sampling from contaminated normal distributions. In I.Olkin et al. (Eds), Contributions to Probability and Statistics. Stanford, CA: Stanford University
  • R.R. Wilcox, (1990), Comparing the means of two independent groups. Biometrical Journal 32, 771-780.
  • R.R. Wilcox, (2001), Fundamentals of Modern Statistical Methods. Springer-Verlag.
  • R.R. Wilcox, (2003), Modern Robust Data Analysis Methods: Measures of Central Tendency. Psychological Methods 8, 254-274.
  • R.R. Wilcox, (2005), Introduction to Robust Estimation and Hypothesis Testing. Elsevier Academic Pres, Second Edition.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

A. F. ÖZDEMİR>

Publication Date June 30, 2010
Published in Issue Year 2010, Volume 3, Issue 1

Cite

Bibtex @research article { jssa123871, journal = {İstatistikçiler Dergisi:İstatistik ve Aktüerya}, issn = {1308-0539}, eissn = {1308-0539}, address = {}, publisher = {Aktüerya Derneği}, year = {2010}, volume = {3}, number = {1}, pages = {8 - 16}, title = {Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal}, key = {cite}, author = {Özdemir, A. F.} }
APA Özdemir, A. F. (2010). Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal . İstatistikçiler Dergisi:İstatistik ve Aktüerya , 3 (1) , 8-16 . Retrieved from https://dergipark.org.tr/en/pub/jssa/issue/10042/123871
MLA Özdemir, A. F. "Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal" . İstatistikçiler Dergisi:İstatistik ve Aktüerya 3 (2010 ): 8-16 <https://dergipark.org.tr/en/pub/jssa/issue/10042/123871>
Chicago Özdemir, A. F. "Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal". İstatistikçiler Dergisi:İstatistik ve Aktüerya 3 (2010 ): 8-16
RIS TY - JOUR T1 - Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal AU - A. F.Özdemir Y1 - 2010 PY - 2010 N1 - DO - T2 - İstatistikçiler Dergisi:İstatistik ve Aktüerya JF - Journal JO - JOR SP - 8 EP - 16 VL - 3 IS - 1 SN - 1308-0539-1308-0539 M3 - UR - Y2 - 2023 ER -
EndNote %0 Journal of Statisticians: Statistics and Actuarial Sciences Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal %A A. F. Özdemir %T Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal %D 2010 %J İstatistikçiler Dergisi:İstatistik ve Aktüerya %P 1308-0539-1308-0539 %V 3 %N 1 %R %U
ISNAD Özdemir, A. F. . "Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal". İstatistikçiler Dergisi:İstatistik ve Aktüerya 3 / 1 (June 2010): 8-16 .
AMA Özdemir A. F. Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal. JSSA. 2010; 3(1): 8-16.
Vancouver Özdemir A. F. Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal. İstatistikçiler Dergisi:İstatistik ve Aktüerya. 2010; 3(1): 8-16.
IEEE A. F. Özdemir , "Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal", İstatistikçiler Dergisi:İstatistik ve Aktüerya, vol. 3, no. 1, pp. 8-16, Jun. 2010