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Robust HEWMA-type estimators for population mean under non-normality

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Abstract

In the field of data science, the performance of a least square estimator is highly affected if the variable under study departs from normality or has the presence of outliers. This study proposes robust HEWMA-type estimators for the population mean by considering some auxiliary information under a non-normality assumption for a time-based survey. The proposed estimators are found to have the minimum mean square errors and biases compared to other relevant estimators for the long-tailed symmetric family. We have investigated the robustness properties of the proposed estimator in presence of the outliers. Finally, the authors provide a simulation study and a real-life application to support the theoretical outcomes of the proposed estimators over the relevant estimators.

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The corresponding author can provide the data generated and/or analyzed during the current study upon a reasonable request.

References

  • Ahmed A, Sanaullah A, Hanif M (2019) A robust alternate to the HEWMA control chart under non-normality. Qual Technol Quant Manag 17(4):423–447. https://doi.org/10.1080/16843703.2019.1662218

    Article  Google Scholar 

  • Cabilio P, Masaro J (1996) A simple test of symmetry about an unknown median. Can J Stat 24:349–361

    Article  Google Scholar 

  • Chhaparwal P, Kumar S (2022) Improving efficiencies of ratio- and product-type estimators for estimating population mean for time-based survey. J Reliab Stat Stud 15(1):325–340

    Google Scholar 

  • Chhaparwal P, Kumar S (2023) Robust ratio and product based estimators using known auxiliary information through modified maximum likelihood. Afr Mat 34:83. https://doi.org/10.1007/s13370-023-01127-8

    Article  MathSciNet  Google Scholar 

  • Choudhury S, Singh BK (2012) A class of chain ratio-cum-dual to ratio type estimator with two auxiliary characters under double sampling in sample surveys. Stat Trans -New Ser 13(3):519–536

    Google Scholar 

  • Cochran WG (1940) The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. J Agric Sci 30(2):262–275

    Article  Google Scholar 

  • Diana G, Giordan M, Perri PF (2011) An improved class of estimators for the population mean. Stat Methods Appl 20:123–140

    Article  MathSciNet  Google Scholar 

  • Gupta S, Shabbir J (2008) On the improvement in estimating the population mean in simple random sampling. J App Stat 35(5):559–566

    Article  MathSciNet  Google Scholar 

  • Gupta S, Shabbir J (2011) On estimating finite population mean in simple and stratified sampling. Commun Statist: Theo Meth 40:199–212

    MathSciNet  Google Scholar 

  • Haq A (2013) A new hybrid exponentially weighted moving average control chart for monitoring process mean. Qual Reliab Eng Int 29(7):1015–1025

    Article  Google Scholar 

  • Haq A (2017) A new hybrid exponentially weighted moving average control chart for monitoring process mean: discussion. Qual Reliab Eng Int 33(7):1629–1631

    Article  Google Scholar 

  • Irfan M, Javed M, Lin Z (2019) Enhanced estimation of population mean in the presence of auxiliary information. J King Saud Univ Sci 31(4):1373–1378

    Article  Google Scholar 

  • Kumar S, Chhaparwal P (2016) A robust dual to ratio estimator for population mean through modified maximum likelihood in simple random sampling. J Appl Probab Stat 11(2):67–82

    Google Scholar 

  • Kumar S, Chhaparwal P (2017) Robust exponential ratio and product type estimators for population mean using order statistics in simple random sampling. Int J Ecol Econ Stat 38(3):51–70

    Google Scholar 

  • Kumar S, Chhaparwal P (2019) Ratio- and product-based estimators using known coefficient of variation of the auxiliary variable via modified maximum likelihood. Life Cycle Reliab Saf Eng 8(2):99–116

    Article  Google Scholar 

  • Kumar S, Chhaparwal P (2021) A simple random sampling modified dual to product estimator for estimating population mean using order statistics. J Mod Appl Stat Methods 19(1):2–32

    Article  Google Scholar 

  • Kumar S, Chhaparwal P (2023) Utilization of priori information in the estimation of population mean for time-based surveys. Ann Data Sci. https://doi.org/10.1007/s40745-023-00472-6

    Article  Google Scholar 

  • Kumar K, Kumar S (2020) Two phase sampling exponential type estimators for population mean using auxiliary attribute in the presence of non-response. Int J Math Stat 21(1):75–85

    MathSciNet  Google Scholar 

  • Kumar S, Kumar S, Oral E (2021) Robust ratio- and product-type estimators under non-normality via linear transformation using certain known population parameters. Ann Data Sci 8(4):733–753. https://doi.org/10.1007/s40745-020-00258-0

    Article  Google Scholar 

  • Kumar S, Chhaparwal P, Kumar K et al (2024) Generalized memory-type estimators for time-based surveys: simulation experience and empirical results with birth weight dataset. Life Cycle Reliab Saf Eng. https://doi.org/10.1007/s41872-023-00239-1

    Article  Google Scholar 

  • Lloyd EH (1952) Least-squares estimation of location and scale parameters using order statistics. Biometrika 39(1/2):88–95

    Article  MathSciNet  Google Scholar 

  • Miao W, Gel YR, Gastwirth JL (2006) A new test of symmetry about an unknown median. In: Hsiung A, Zhang C-H, Ying Z (eds) Random Z. walk, sequential analysis and related topics: a festschrift in honor of Yuan-Shih Chow. World Scientific Publisher, Singapore, pp 199–214

    Chapter  Google Scholar 

  • Mira A (1999) Distribution-free test for symmetry based on Bonferroni’s measure. J Appl Stat 26:959–972

    Article  MathSciNet  Google Scholar 

  • Noor-ul-Amin M (2020) Memory type ratio and product estimators for population mean for time-based surveys. J Stat Comput Simul 90(17):3080–3092. https://doi.org/10.1080/00949655.2020.1795660

    Article  MathSciNet  Google Scholar 

  • Olson DL, Shi Y (2007) Introduction to business data mining. McGraw-Hill/Irwin, New York

    Google Scholar 

  • Oral E, Kadilar C (2011) Robust ratio-type estimators in simple random sampling. J Kor Statis Soc 40:457–467

    Article  MathSciNet  Google Scholar 

  • Oral E, Oral E (2011) A robust alternative to the ratio estimator under non-normality. Statist Prob Lett 81:930–936

    Article  MathSciNet  Google Scholar 

  • Puthenpura S, Sinha NK (1986) Modified maximum likelihood method for the robust estimation of system parameters from very noisy data. Automatica 22:231–235

    Article  Google Scholar 

  • Rao JNK, Beegle LD (1967) A Monte Carlo study of some ratio estimators. Sankhya Ser B 29:47–56

    MathSciNet  Google Scholar 

  • Shi Y (2022) Advances in big data analytics: theory, algorithm and practice. Springer, Singapore

    Book  Google Scholar 

  • Shi Y, Tian YJ, Kou G, Peng Y, Li JP (2011) Optimization based data mining: theory and applications. Springer, Berlin

    Book  Google Scholar 

  • Singh HP, Solanki RS (2012) An alternative procedure for estimating the population mean in simple random sampling. Pak J Stat Oper Res 8(2):213–232

    Article  MathSciNet  Google Scholar 

  • Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Ann Data Sci 4(2):149–178

    Article  Google Scholar 

  • Tiku ML, Akkaya AD (2004) Robust estimation and hypothesis testing. New Age International (P) Limited, New Delhi

    Google Scholar 

  • Tiku ML, Bhasln P (1982) Usefulness of robust estimators in sample survey. Commun Statist: Theo Meth 11:2597–2610

    Article  MathSciNet  Google Scholar 

  • Tiku ML, Kumra S (1981) Expected values and variances and covariances of order statistics for a family of symmetric distributions (student’s t). Selected tables in mathematical statistics, vol 8. Amer Math Soc, pp 141–270

    Google Scholar 

  • Tiku ML, Suresh RP (1992) A new method of estimation for location and scale parameters. J Stat Plann Infer 30:281–292

    Article  MathSciNet  Google Scholar 

  • Tiku ML, Vellaisamy P (1996) Improving efficiency of survey sample procedures through order statistics. J Ind Soc Agric Stat 49:363–385

    Google Scholar 

  • Tsay RS (2010) Analysis of financial time series. Wiley, New Jersey

    Book  Google Scholar 

  • Vaughan DC (1992) Expected values, variances and covariances of order statistics for student’s t-distribution with two degrees of freedom. Commun Statist-Simul Comput 21:391–404

    Article  Google Scholar 

  • Vaughan DC, Tiku ML (2000) Estimation and hypothesis testing for non normal bivariate distribution with applications. Math Comp Model 32:53–67

    Article  Google Scholar 

Download references

Acknowledgements

The authors are heartily thankful to the editors and the referees for their constructive comments on bringing the original manuscript to its present form.

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  1. Department of Statistics, Central University of Rajasthan, Kishangarh, Ajmer, Rajasthan, India

    Akanksha Jakhar & Sanjay Kumar

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  1. Akanksha Jakhar
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  2. Sanjay Kumar
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Correspondence to Sanjay Kumar.

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Jakhar, A., Kumar, S. Robust HEWMA-type estimators for population mean under non-normality. Life Cycle Reliab Saf Eng 13, 33–49 (2024). https://doi.org/10.1007/s41872-024-00244-y

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