118
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

An effective approach to linear calibration estimation with its applications

, &
Pages 5154-5174 | Received 18 Jul 2018, Accepted 29 Apr 2019, Published online: 13 May 2019

References

  • Aitchison, J., and I. R. Dunsmore. 1975. Statistical prediction analysis. UK: Cambridge University Press.
  • Alsuwyeh, A. A., F. Alanazi, F. Shakeel, M. M. Salem-Bekhit, and N. Haq. 2018. Estimation of anti-neoplastic drug doxorubicin in bacterial ghost matrix by new “environmentally benign” RP-HPLC method: A step towards sustainable development of pharmaceutical industry. Arabian Journal for Science and Engineering 43 (1):181–90. doi: 10.1007/s13369-017-2664-2.
  • An, S., and Y. B. Gianchandani. 2014. A dynamic calibration method for Pirani gauges embedded in fluidic networks. Journal of Microelectromechanical Systems 23 (3):699–709. doi: 10.1109/JMEMS.2013.2281319.
  • Andriamahenina, N. N., E. O. Rasoazanany, H. N. Ravoson, L. V. Rakotozafy, M. Harinoely, R. Andraimbololona, and R. Edmond. 2018. Dealing with outlier in linear calibration curves: a case study of graphite furnace atomic absorption spectrometry. World Journal of Applied Chemistry 3 (1):10.
  • Azhar, A. H., M. Masood, G. Nabi, and M. Basharat. 2014. Performance evaluation of reference evapotranspiration equations under semiarid Pakistani conditions. Arabian Journal for Science and Engineering 39 (7):5509–20. doi: 10.1007/s13369-013-0817-5.
  • Berkson, J. 1969. Estimation of a linear function for a calibration line; consideration of a recent proposal. Technometrics 11 (4):649–60. doi: 10.1080/00401706.1969.10490728.
  • Blas, B.,. H. Bolfarine, and V. H. Lachos. 2013. Statistical analysis of controlled calibration model with replicates. Journal of Statistical Computation and Simulation 83 (5):941–61.
  • Bo, L., F. Yan-Hong, C. Yong, C. Wei-Wei, W. Yu-Sa, X. Yu-Peng, and Z. Ya. 2014. A linear calibration method on DNL error for energy spectrum. arXiv preprint arXiv:1404.6303.
  • Box, G. E. P., and D. R. Cox. 1964. An analysis of transformations. Journal of the Royal Statistical Society (B) 26:211–52. doi: 10.1111/j.2517-6161.1964.tb00553.x.
  • Box, G. E. P., and P. W. Tidwell. 1962. Transformation of the independent variables. Technometrics 4 (4):531–50. doi: 10.1080/00401706.1962.10490038.
  • Brown, G. H. 1979. An optimization criterion for linear inverse estimation. Technometrics 21 (4):575–9. doi: 10.1080/00401706.1979.10489829.
  • Brown, P. J. 1982. Multivariate calibration (with discussion). Journal of the Royal Statistical Society (B) 44:287–321. doi: 10.1111/j.2517-6161.1982.tb01209.x.
  • Brümmer, N., A. Swart, and D. van Leeuwen. 2014. A comparison of linear and non-linear calibrations for speaker recognition. arXiv preprint arXiv:1402.2447.
  • Darwish, H. W., and A. H. Backeit. 2013. Multivariate versus classical univariate calibration methods for spectrofluorimetric data: application to simultaneous determination of olmesartan medoxamil and amlodipine besylate in their combined dosage form. Journal of Fluorescence 23 (1):79–91. doi: 10.1007/s10895-012-1119-0.
  • Ding, K., and R. J. Karunamuni. 2004. A linear empirical Bayes solution for the calibration problem. Journal of Statistical Planning and Inference 119 (2):421–47. doi: 10.1016/S0378-3758(02)00492-5.
  • Gang, Y., Z. Yingtang, F. Hongbo, Z. Guang, and R. Guoquan. 2014. Linear Calibration Method of Magnetic Gradient Tensor System. Measurement 56:8–18. doi: 10.1016/j.measurement.2014.06.017.
  • Halima, Z., and D. Abdelnasser. 2016. Exponential inequalities in linear calibration problem. Communications in Statistics-Theory and Methods 45 (18):5251–62.
  • Hassini, A., and A. H. Belbachir. 2015. A simple remote sensing ground receiving system for interest creation in systems engineering and geophysics research. Arabian Journal for Science and Engineering 40 (6):1793–808. doi: 10.1007/s13369-015-1640-y.
  • Hernández, N., R. J. Biscay, and I. Talavera. 2012. A non-Bayesian predictive approach for statistical calibration. Journal of Statistical Computation and Simulation 82 (4):529–45. doi: 10.1080/00949655.2010.545060.
  • Hunter, W. G., and W. F. Lamboy. 1981. A Bayesian analysis of the linear calibration problem (with discussion). Technometrics 23 (4):323–50. doi: 10.1080/00401706.1981.10487672.
  • Jensen, D. R., and D. E. Ramirez. 2013. Irregularities in X (Y) from Y (X) in linear calibration. Journal of Statistical Computation and Simulation 83 (10):1807–28. doi: 10.1080/00949655.2012.671324.
  • Kannan, N., P. K. Jerome, and L. M. Robert. 2007. A comparison of Classical and inverse estimators in the calibration problem. Communications in Statistics - Theory and Methods 36 (1):83–95. doi: 10.1080/03610920600966225.
  • Krutchkoff, R. G. 1967. Classical and inverse regression methods of calibration. Technometrics 9 (3):425–39. doi: 10.1080/00401706.1967.10490486.
  • Kubokawa, T., and C. P. Robert. 1994. New perspectives on linear calibration. Journal of Multivariate Analysis 51 (1):178–200. doi: 10.1006/jmva.1994.1056.
  • Liao, J. J. 2002. An insight into linear calibration: univariate case. Statistics & Probability Letters 56:271–81. doi: 10.1016/S0167-7152(01)00190-0.
  • Lwin, T. 1985. Calibration with supplementary information. Proc. Inter Stat.Institute, 45th session contributed papers, 12-22 August, Amsterdam. pp. 65–66.
  • Lwin, T., and J. S. Maritz. 1980. A note on the problem of statistical calibration. Applied Statistics 29 (2):135–41. doi: 10.2307/2986298.
  • Lwin, T., and J. S. Maritz. 1982. An analysis of the linear-calibration controversy from the perspective of compound estimation. Technometrics 24 (3):235–42. doi: 10.1080/00401706.1982.10487764.
  • Marciano, F. W. P., B. G. Blas Achic, and F. J. A. Cysneiros. 2016. Symmetrical linear calibration model to replicated data. Chilean Journal of Statistics (ChJS) 7(1).
  • Muhammad, F., and A. D. McLaren. 1985. An approach to linear calibration. Proc. Inter. Stat. Institute, 45th session contributed papers, 12-22 August, Amsterdam. pp. 15-16.
  • Muhammad, F., and M. Riaz. 2016. An improved approach to multivariate linear calibration. Scientia Iranica 23 (3):1355–69. doi: 10.24200/sci.2016.3903.
  • Naeini, M. P., and G. F. Cooper. 2018. Binary classifier calibration using an ensemble of piecewise linear regression models. Knowledge and Information Systems 54 (1):151–70. doi: 10.1007/s10115-017-1133-2.
  • Nyström, M., R. Andersson, K. Holmqvist, and J. van de Weijer. 2013. The influence of calibration method and eye physiology on eyetracking data quality. Behavior Research Methods 45 (1):272–88. doi: 10.3758/s13428-012-0247-4.
  • Oman, S. D. 1985. An exact formula for mean squared error of the inverse estimator in a linear calibration problem. Journal of Statistical Planning and Inference 11(2):189–96. doi: 10.1016/0378-3758(85)90005-9.
  • Raposo, F. 2016. Evaluation of analytical calibration based on least-squares linear regression for instrumental techniques: A tutorial review. TrAC Trends in Analytical Chemistry 77:167–85. doi: 10.1016/j.trac.2015.12.006.
  • Ratrout, N. T., S. M. Rahman, and I. Reza. 2015. Calibration of PARAMICS model: Application of artificial intelligence-based approach. Arabian Journal for Science and Engineering 40 (12):3459–68. doi: 10.1007/s13369-015-1816-5.
  • Sharma, B., S. K. Sharma, S. M. Gupta, and A. Kumar. 2018. Modified two-step method to prepare long-term stable CNT nanofluids for heat transfer applications. Arabian Journal for Science and Engineering:1–9.
  • Shukla, G. K., and P. Datta. 1985. Comparison of the inverse estimator with the classical estimator subject to preliminary test in linear calibration. Journal of Statistical Planning and Inference 12:93–102. doi: 10.1016/0378-3758(85)90057-6.
  • Tallis, G. M. 1969. Note on a calibration problem. Biometrika 56 (3):505–8. doi: 10.1093/biomet/56.3.505.
  • Wimmer, G., and V. Witkovský. 2007. Univariate linear calibration via replicated errors-in-variables model. Journal of Statistical Computation and Simulation 77 (3):213–27. doi: 10.1080/10629360600679433.
  • Yap, X. Q., and M. Hashim. 2013. A robust calibration approach for PM 10 prediction from MODIS aerosol optical depth. Atmospheric Chemistry and Physics 13 (6):3517–26. doi: 10.5194/acp-13-3517-2013.
  • Zhao, G., and X. Xu. 2017. Uniformly most powerful unbiased test in univariate linear calibration. Statistics 51 (3):609–14. doi: 10.1080/02331888.2016.1265968.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.