© Housila P. Singh, Rajesh Tailor, Priyanka Malviya. Article available under the CC BY-SA 4.0 licence
ARTICLE
ABSTRACT
This paper addresses the problem of estimating the finite population variance of the study variable y using information on the known population variance of the auxiliary variable x in sample surveys. We have suggested a class of estimators for population variance using information on population variance of x. The bias and mean squared error of the suggested class of estimators up to first order of approximation was obtained. Preference regions were derived under which the suggested class of estimators is more efficient than the usual unbiased estimator, Das and Tripathi (1980) estimators, Isaki (1983) ratio estimator, Singh et al (1973, 1988) estimator and Gupta and Shabbir (2007) estimator. An empirical study as well as simulation study were carried out in support of the present study.
KEYWORDS
study variable, auxiliary variable, class of estimators, bias, mean squared error.
REFERENCES
Adhvaryu, D., Gupta, P. C., (1983). On some alternative sampling strategies using auxiliary information. Metrika, 30, pp. 217–226.
Bahl, S., Tuteja, R. K., (1991). Ratio and product type exponential estimators. Journal of Information and Optimization Sciences, 12, 1, pp. 159–164.
Cochran, W. G., (1940). The estimation of the yields of the cereal experiments by sampling for the ratio of grain to total produce. The Journal of Agricultural Science, 30, pp. 262–275.
Das, A. K., (1982). Contributions to the theory of sampling strategies based on auxiliary information. Ph.D. Thesis, B. C. K. V., Mohanpur, Nadia, West Bengal, India.
Das, A. K., Tripathi, T. P., (1978). Use of auxiliary information in estimating the finite population variance. Sankhya, C(40), pp. 139–148.
Das, A. K., Tripathi, T. P., (1980). Sampling strategies for population mean when the coefficient of variation of an auxiliary character is known, Sankhya, C(42), pp. 76–86.
Gupta, P. C., (1978). On some quadratic and higher degree ratio and product estimator. Journal of Indian Society of Agriculture Statistics, 30, pp. 71–80.
Gupta, S., Shabbir, J., (2007). On the use of transformed auxiliary variables in estimating population mean. Journal of Statistical Planning and Inference, 137(5), pp. 1606–1611.
Isaki, C. T., (1983). Variance estimation using auxiliary information. Journal of the American Statistical Association, 78, pp. 117–123.
Kadilar, C., Cingi, H., (2007). Improvement in variance estimation in simple random sampling. Communications in Statistics Theory Methods, 36(11), pp. 2075–2081.
Pal S. K., Singh, H. P., (2018). Improved estimators of the finite universe variance and mean using auxiliary variable in sample surveys. International Journal of Mathematics and Computation, 29(2), pp. 58–70.
Ray, S. K., Singh, R. K., (1981). Difference cum ratio type estimators. Jour. Ind. Sta. Assoc., 19, pp. 147–151.
Reddy, V. N., (1978). A study on the use of prior knowledge on certain population parameters in estimation. Sankhya, C (40), pp. 29–37.
Robson, D. S., (1957). Application of multivariate polykays to the theory of unbiased ratio-type estimation. Journal of American Statistical Association, 52, pp. 511–522.
Sahai, A., Sahai, A., (1985). On efficient use of auxiliary information. Journal of Statistical Planning and Inference, 12, pp. 203–212.
Searls, D. T., Intrapanich, R., (1990). A note on an estimator for variance that utilizes the kurtosis. The American Statistician, 44(4), pp. 295–296.
Singh J., Pandey, B. N. and Hirano, K., (1973). On the utilization of a known coefficient of kurtosis in estimation procedure of variance. Annals of the Institute of Statistical Mathematics, 25, pp. 51–55.
Singh, H. P., Ruiz Espejo, M., (2003). On Linear regression and ratio-product estimation of a finite population mean. The Statistician, 52, 1, pp. 59–67.
Singh, H. P., Solanki, R. S., (2013a). Improved estimation of finite population variance using auxiliary information. Communications in Statistics Theory Methods, 42, pp. 2718–2730.
Singh, H. P., Solanki, R. S., (2013b). A new procedure for variance estimation in simple random sampling using auxiliary information. Statistical Papers, 54, 2, pp. 479–497.
Singh, H. P., Tailor, R., (2005). Estimation of finite population mean using known correlation coefficient between auxiliary characters. Statistica, 65, 4, pp. 407–418.
Singh, H. P., (1987). Class of almost unbiased ratio and product type estimators for finite population mean applying quenocillles method. Journal of Indian Society of Agriculture Statistics, 39, pp. 280–288.
Singh, H. P., Upadhyaya, L. N. and Lachan, R., (1988). Estimation of finite population variance. Current Science, 57, 24, pp. 1331–1334.
Singh, H. P., (1986). A generalized class of estimators of ratio, product and mean using supplementary information on an auxiliary character in PPSWR sampling scheme. Gujarat Statistical Review, 13(2), pp. 1–30.
Singh, H. P., Nigam, P., (2020). A general class of dual to ratio estimators. Pakistan Journal of Statisticas and Operation Research,16, 3, pp. 421–431.
Singh, H. P., Upadhyaya, L. N., (1986). A dual to modified ratio estimators using coefficient of variation of auxiliary variable. Proceedings of the National Academy of Sciences, 56, A, pp. 336–340.
Singh, H. P., Yadav, A., (2020). A new exponential approach for reducing the mean squared errors of the estimators of population mean using conventional and non-conventional location parameters. Journal of Modern Applied Statistical Methods, 18(1), pp. 1–47.
Singh, H. P., Tailor, R. and Tailor, R., (2012). Estimation of finite population mean in two-phase sampling with known coefficient of variation of an auxiliary character. Statistica, 72(1), pp. 111–126.
Singh, J., Pandey, B. N. and Hirano, K., (1973). On the utilization of a known coefficient of kurtosis in the estimation procedure of variance. Annals of the Institute of Statistical Mathematics, 25, pp. 51–55.
Singh, M. P., (1965). On the estimation of ratio and product of the population parameters. Sankhya, B (27), pp. 321–328.
Singh, M. P., (1967). Ratio-cum-product method of estimation. Metrika, 12, 1, pp. 34–43.
Singh, R. K., Singh, G., (1984). A class of estimators for population variance using information on two auxiliary variates. Aligarh Journal of Statistics, 3&4, pp. 43–49.
Singh, S., (2003). Advanced sampling theory with application: How Micheal “selected” A my, Kluwer Academic Publishers.
Solanki, R. S., Singh, H. P., (2013). An improved class of estimators for population variance. Model Assisted Statistics and Application, 8, 3, pp. 229–238.
Srivastava, S. K., (1971). A generalized estimator for the mean of a finite population using multi-auxiliary information. Journal of American Statistical Association, 66, pp. 404–407.
Srivastava, S. K., (1980). A class of estimators using auxiliary information in sample surveys. The Canadian Journal of Statistics, 8, 2, pp. 253–254.
Srivastava, S. K., Jhajj, H. S., (1980). A class of estimators using auxiliary information for estimating finite population variance. Sankhya, C(42), pp. 87–96.
Tracy, D. S., Singh, H. P. and Singh, R., (1996). An alternative to the ratio-cum-product estimator in sample surveys. Journal of Statistical Planning and Inference, 53, 3, pp. 375–387.
Vos, J. W. E., (1980). Mixing of direct, ratio and product methods estimators. Statist. Netherlands Society for Statistics and Operations Research, 34, 4, pp. 209–218.
Walsh, J. E., (1970). Generalisation of ratio estimate for population total. Sankhya, A(33), pp. 99–106.
Yadav, R., Upadhyaya, L. N., Singh, H. P. and Chatterjee, S., (2013). A generalized family of transformed ratio product estimator for variance in sample surveys. Communications in Statistics Theory and Methods, 42(10), pp. 1839–1850.