Estimation of finite population distribution function with auxiliary information in a complex survey sampling

Mohsin Abbas; Abdul Haq

Ayuda

Estimation of finite population distribution function with auxiliary information in a complex survey sampling

Mohsin Abbas ^[1] ; Abdul Haq ^[1]
1. [1] Quaid-i-Azam University
  
  Quaid-i-Azam University
  
  Pakistán
Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 46, Nº. 1, 2022, págs. 67-94
Idioma: inglés
Enlaces
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Resumen
- In this paper, we consider the problem of estimating the finite population cumulative distribution function (CDF) in a complex survey sampling, which includes two-stage and three-stage cluster sampling schemes with and without stratification. We propose two new families of CDF estimators using supplementary information on a single auxiliary variable. Explicit mathematical expressions of the biases and mean squared errors of the proposed CDF estimators are developed under the first order of the approximation. Real datasets are also considered to support the proposed theory.
Referencias bibliográficas
- Berger, Y. G. and MunÌoz, J. F. (2015). On estimating quantiles using auxiliary information. Journal of Offcial Statistics, 31(1):101–119.
- Chambers, R. L. and Dunstan, R. (1986). Estimating distribution functions from survey data. Biometrika, 73(3):597–604.
- Cochran, W. G. (1977). Sampling Techniques, 3rd Edition. John Wiley.
- Deville, J.-C. and SaÌrndal, C.-E. (1992). Calibration estimators in survey sampling. Journal of the American Statistical Association, 87(418):376–382.
- Francisco, C. A. and Fuller, W. A. (1986). Estimation of the distribution function with a complex survey. In JSM Proceedings, Survey Research...
- Hansen, M. H. and Hurwitz, W. N. (1943). On the theory of sampling from fnite populations. The Annals of Mathematical Statistics, 14(4):333–362.
- Haq, A. (2017a). Estimation of the distribution function under hybrid ranked set sampling. Journal of Statistical Computation and Simulation,...
- Haq, A. (2017b). Two-stage cluster sampling with hybrid ranked set sampling in the secondary sampling frame. Communications in Statistics-Theory...
- Haq, A., Abbas, M., and Khan, M. (2021). Estimation of fnite population distribution function in a complex survey sampling. Communications...
- Hussain, S., Ahmad, S., Saleem, M., and Akhtar, S. (2020). Finite population distribution function estimation with dual use of auxiliary information...
- Khoshnevisan, M., Singh, R., Chauhan, P., and Sawan, N. (2007). A general family of estimators for estimating population mean using known...
- Lee, S. E., Lee, P. R., and Shin, K.-I. (2016). A composite estimator for stratifed two stage cluster sampling. Communications for Statistical...
- MartÄ±Ìnez, S., Rueda, M., Arcos, A., and MartÄ±Ìnez, H. (2010). Optimum calibration points estimating distribution functions. Journal of...
- MartÄ±Ìnez, S., Rueda, M., and Illescas, M. (2022). The optimization problem of quantile and poverty measures estimation based on calibration....
- Mayor-Gallego, J. A., Moreno-Rebollo, J. L., and JimeÌnez-Gamero, M. D. (2019). Estimation of the fnite population distribution function...
- Murthy, M. N. (1967). Sampling Theory and Methods. Calcutta-35: Statistical Publishing Society.
- Nafu, L., Oshungade, I., and Adewara, A. (2012). Alternative estimation method for a three-stage cluster sampling in fnite population. American...
- Nematollahi, N., M, M. S., and Saba, R. A. (2008). Two-stage cluster sampling with ranked set sampling in the secondary sampling frame. Communications...
- Rao, J., Kovar, J., and Mantel, H. (1990). On estimating distribution functions and quantiles from survey data using auxiliary information....
- Rustagi, R. K. (1978). Some theory of the prediction approach to two stage and stratifed two stage cluster sampling. PhD thesis, The Ohio...
- Sahoo, L. (1987). A regression-type estimator in two-stage sampling. Calcutta Statistical Association Bulletin, 36(1-2):97–100.
- SaÌrndal, C.-E., Swensson, B., and Wretman, J. (2003). Model Assisted Survey Sampling. Springer Science & Business Media.
- Singh, H. P., Singh, S., and Kozak, M. (2008). A family of estimators of fnite-population distribution function using auxiliary information....
- Singh, R., Chauhan, P., Sawan, N., and Smarandache, F. (2009). Improvement in estimating the population mean using exponential estimator in...
- Smith, T. (1969). A note on ratio estimates in multistage sampling. Journal of the Royal Statistical Society: Series A (General), 132(3):426–430.
- Srivastava, M. and Garg, N. (2009). A general class of estimators of a fnite population mean using multi-auxiliary information under two stage...
- Stokes, S. L. and Sager, T. W. (1988). Characterization of a ranked-set sample with application to estimating distribution functions. Journal...
- Sukhatme, P. V., Sukhatme, B., Sukhatme, S., and Asok, C. (1984). Sampling theory with applications. Indian Society of Agricultural Statistics,...
- Tarima, S. and Pavlov, D. (2006). Using auxiliary information in statistical function estimation. ESAIM: Probability and Statistics, 10:11–23.
- Yaqub, M. and Shabbir, J. (2020). Estimation of population distribution function involving measurement error in the presence of non response....