Skip to main content

Imputation of the Missing Data

  • Chapter
  • First Online:
  • 1427 Accesses

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

Abstract

We may consider the existence of missing observations as unimportant, considering that the risk of misunderstanding is negligible. The surveyor assumes some model that allows adequately explaining the variable of interest. In such cases, we are able to predict the unknown values and to plug them into some estimator. Generally, the models used for imputing in sampling are not complicated and rely on simple ideas. Imputation in simple random sampling has been developed for decades; the literature is increased yearly. Ranked Set Sampling (RSS) alternatives are presented in this chapter. The efficiency of this approach is supported for the different models. On some occasions the preference of RSS is doubtful and needs numerical comparisons.

Let us act on what we have, since we have not what we wish.

Cardinal Newman

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Al-Nasser, D. A. (2007): L-ranked set sampling: A generalization procedure for robust visual sampling. Communications in Statistics: Simulation and Computation, 6, 33–43.

    Google Scholar 

  • Al-Omari, A. I., & Jaber, K. (2008). Percentile double ranked set sampling. Journal of Mathematics and Statistics, 4, 60–64.

    MATH  Google Scholar 

  • Al-Omari, A. I., JABER, K., & Al-Omari, A. (2008). Modified ratio-type estimators of the mean using extreme ranked set sampling. Journal of Mathematics and Statistics, 4, 150–155.

    Article  MATH  Google Scholar 

  • Al-Omari, A. I., Jemain, A. A., & Ibrahim, K. (2009). New ratio estimators of the mean using simple random sampling and ranked set sampling methods. Revista Investigación Operacional, 30, 97–108.

    MathSciNet  MATH  Google Scholar 

  • Bai, Z. D., & Chen, Z. (2003). On the theory of ranked set sampling and its ramifications. Journal of Statistical Planning and Inference, 109, 81–99.

    Article  MathSciNet  MATH  Google Scholar 

  • Bouza-Herrera C. N. (2012). Estimation of the population mean under l ranked set sampling with missing observations, aproved for publication in. International Journal of Statistics and Probability. doi10.1155/2012/214959

  • Bouza, C. N., & Al-Omari, A. I. (2011a). Ranked set estimation with imputation of the missing observations: the median estimator. Revista Investigación Operacional, 2, 30–37.

    Google Scholar 

  • Bouza, C. N., & Al-Omari, A. I. (2011b). Ratio imputation of missing data in ranked set sampling. Submitted to statistics, gsta-2011-0026.r2.

    Google Scholar 

  • Bouza, C. N., & Al-Omari, A. I. (2013). Imputation methods of missing data for estimating the population mean using simple random sampling with known correlation coefficient. Accepted by Quality and Quantity, 47, 353–365. doi 10.1007/s11135-011-9522-1.

  • Bouza, C. N., & Al-Omari, A. I. (2011c). Estimating the population mean in the case of missing data using simple random sampling. To be published in statistics, doi10.1080/02331888.2010.505654.

  • Bouza, C. N. (2008a). Estimation of the population mean with missing observations using product type estimators. Revista Investigación Operacional, 29, 207–223.

    Google Scholar 

  • Chang, H. J., & Huang, K. (2008). Ratio estimation in survey sampling when some observations are missing. International Journal of Information and Management Sciences, 12, 1–9.

    Article  MathSciNet  Google Scholar 

  • Chang, H. J., & Huang, K. (2000b). On estimation of ratio of populatoin means in survey sampling when some observations are missing. Journal of Information & Optimization Sciences, 21, 429–436.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, Z., Bai, Z., & Sinha, B. K. (2004). Ranked set sampling: theory and applications. Lectures notes in statistics, p. 176. New York: Springer.

    Google Scholar 

  • Jemain, A. A., & Al-Omari, A. I. (2006). Multistage median ranked set samples for estimating the population mean. Pakistan Journal of Statistics, 22, 195–207.

    MathSciNet  MATH  Google Scholar 

  • Kadilar, C., & Cingi, H. (2008). Estimators for the population mean in the case of missing data. Communication in Statistics: Theory and Methods, 37, 2226–2236.

    Article  MathSciNet  MATH  Google Scholar 

  • Liu, L., TUA, Y., LIB, Y., & ZOU, G. (2006). Imputation for missing data and variance estimation when auxiliary information is incomplete. Model Assisted Statistics and Applications, 1, 83–94.

    MATH  Google Scholar 

  • Mutllak, H. A. (1997). Median ranked set sampling. Journal of Applied Statistical Sciences, 6, 245–255.

    Google Scholar 

  • Muttlak, H. A. (2003). Investigating the use of quartile ranked set samples for estimating the population mean. Journal of Applied Mathematics and Computation, 146, 437–443.

    Article  MathSciNet  MATH  Google Scholar 

  • Young-Jae, M. (2005). Monotonicity conditions and inequality imputation for sample and non-response problems. Econometric Reviews, 24, 175–194.

    Article  MathSciNet  Google Scholar 

  • Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581–582.

    Article  MathSciNet  MATH  Google Scholar 

  • Rueda, M., & González, S. (2004). Missing data and auxiliary information in surveys. Computational Statistics, 10, 559–567.

    Google Scholar 

  • Rueda, M., Martínez, S., Martínez, H., & Arcos, A. (2006). Mean estimation with calibration techniques in presence of missing data. Computational Statistics and Data Analysis, 50, 3263–3277.

    Google Scholar 

  • Samawi, H. M., & Muttlak, H. A. (1996). Estimation of ratio using rank set sampling. Biometrical Journal, 36, 753–764.

    Article  MathSciNet  Google Scholar 

  • Singh, S., & Deo, B. (2003). Imputation by power transformation. Statistical Papers, 44, 555–579.

    Article  MathSciNet  MATH  Google Scholar 

  • Singh, S., & Horn, S. (2000). Compromised imputation in survey sampling. Metrika, 51, 267–276.

    Article  MathSciNet  MATH  Google Scholar 

  • Takahasi, K., & Wakimoto, K. (1968). On unbiased estimates of population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics, 20, 1–31.

    Google Scholar 

  • Toutenburg, H., Srivastava, V. K., & SHALABH, V. (2008). Amputation versus imputation of missing values through ratio method in sample surveys. Statistical Papers, 49, 237–247.

    Article  MathSciNet  MATH  Google Scholar 

  • Tsukerman, E. V. (2004). Optimal linear estimation of missing observations (in Russian). Studies in information science. Kazan. Lzd. Otechetsvo, 2, 77–96.

    MathSciNet  Google Scholar 

  • Zou, U., Feng, S., & Qin, H. (2002). Sample rotation with missing data. Science in China Series A, 45, 42–63.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carlos N. Bouza-Herrera .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 The Author(s)

About this chapter

Cite this chapter

Bouza-Herrera, C.N. (2013). Imputation of the Missing Data. In: Handling Missing Data in Ranked Set Sampling. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39899-5_4

Download citation

Publish with us

Policies and ethics