Estimation after selection from bivariate normal population with application to poultry feeds data

Year 2022, Volume: 51 Issue: 4, 1141 - 1159, 01.08.2022

Mohd. Arshad Omer Abdalghani K. R. Meena Ashok Pathak

https://doi.org/10.15672/hujms.936367

Cited By: 1

Abstract

In many practical situations, it is often desired to select a population (treatment, product, technology, etc.) from a choice of several populations on the basis of a particular characteristic that associated with each population, and then estimate the characteristic associated with the selected population. The present paper is focused on estimating a characteristic of the selected bivariate normal population, using a LINEX loss function. A natural selection rule is used for achieving the aim of selecting the best bivariate normal population. Some natural-type estimators and Bayes estimator (using a conjugate prior) of a parameter of the selected population are presented. An admissible subclass of equivariant estimators, using the LINEX loss function, is obtained. Further, a sufficient condition for improving the competing estimators is derived. Using this sufficient condition, several estimators improving upon the proposed natural estimators are obtained. Further, an application of the derived results is provided by considering the poultry feeds data. Finally, a comparative study on the competing estimators of a parameter of the selected population is carried-out using simulation.

Keywords

Estimation after selection, bivariate normal distribution, improved estimators, LINEX loss function, natural selection rule

References

• [1] M. Amini and N. Nematollahi, Estimation of the parameters of a selected multivariate population, Sankhya A 79 (1), 13-38, 2017.
• [2] M. Arshad and O. Abdalghani, Estimation after selection from uniform populations under an asymmetric loss function, Amer. J. Math. Manage. Scie. 38 (4), 349362, 2019.
• [3] M. Arshad and O. Abdalghani, On estimating the location parameter of the selected exponential population under the LINEX loss function, Braz. J. Probab. Stat. 34 (1), 167-182, 2020.
• [4] M. Arshad and N. Misra, Selecting the exponential population having the larger guarantee time with unequal sample sizes, Comm. Statist. Theory Methods 44 (19), 4144- 4171, 2015.
• [5] M. Arshad and N. Misra, Estimation after selection from uniform populations with unequal sample sizes, Amer. J. Math. Manage. Scie, 34 (4), 367-391, 2015.
• [6] M. Arshad and N. Misra, Estimation after selection from exponential populations with unequal scale parameters, Statist. Papers 57 (3), 605-621, 2016.
• [7] M. Arshad and N. Misra, On estimating the scale parameter of the selected uniform population under the entropy loss function, Braz. J. Probab. Stat. 31 (2), 303-319, 2017.
• [8] M. Arshad, N. Misra and P. Vellaisamy, Estimation after selection from gamma populations with unequal known shape parameters, J. Stat. Theory Pract. 9 (2), 395-418, 2015.
• [9] J.F. Brewster and Z.V. Zidek, Improving on equivariant estimators, Ann. Statist. 2 (1), 21-38, 1974.
• [10] A. Cohen and H.B. Sackrowitz, Estimating the mean of the selected population, in S.S. Gupta and J.O. Berger (ed.) Statistical Decision Theory and Related Topics-III, 1st ed., 243-270, 1982.
• [11] R.C. Dahiya, Estimation of the mean of the selected population, J. Amer. Statist. Assoc. 69 (345), 226-230, 1974.
• [12] C. Fuentes, G. Casella and M.T. Wells, Confidence intervals for the means of the selected populations, Electron. J. Stat. 12 (1), 58-79, 2018.
• [13] S. Korkmaz, D. Goksuluk and G. Zararsiz, MVN: An R package for assessing multivariate normality, R Journal 6 (2), 151-162, 2014.
• [14] X. Lu, A. Sun and S.S. Wu, On estimating the mean of the selected normal population in two-stage adaptive designs, J. Statist. Plann. Inference 143 (7), 1215-1220, 2013.
• [15] K.R. Meena, M. Arshad and A.K. Gangopadhyay, Estimating the parameter of selected uniform population under the squared log error loss function, Comm. Statist. Theory Methods 47 (7), 1679-1692, 2018.
• [16] K.R. Meena and A.K. Gangopadhyay, Estimating volatility of the selected security, Amer. J. Math. Manage. Scie. 36 (3), 177-187, 2017.
• [17] K.R. Meena and A.K. Gangopadhyay, Estimating parameter of the selected uniform population under the generalized stein loss function, Appl. Appl. Math. 15 (2), 894- 915, 2020.
• [18] K.R. Meena, A.K. Gangopadhyay and O. Abdalghani, On estimating scale parameter of the selected Pareto population under the generalized Stein loss, Amer. J. Math. Manage. Scie. 40 (4) 357-377, 2021.
• [19] N. Misra and M. Arshad, Selecting the best of two gamma populations having unequal shape parameters, Stat. Methodol. 18, 41-63, 2014.
• [20] N. Misra and I.D. Dhariyal, Non-minimaxity of natural decision rules under heteroscedasticity, Statistics & Decisions 12, 79-89, 1994.
• [21] N. Misra and E.C. van der Meulen, On estimation following selection from nonregular distributions, Comm. Statist. Theory Methods 30 (12), 2543-2561, 2001.
• [22] N. Misra and E.C. van der Meulen, On estimating the mean of the selected normal population under the LINEX loss function, Metrika 58 (2), 173183, 2003.
• [23] Z. Mohammadi and M. Towhidi, Estimating the parameters of a selected bivariate normal population, Statist. Probab. Lett. 122, 205-210, 2017.
• [24] N. Nematollahi and M.J. Jozani, On risk unbiased estimation after selection, Braz. J. Probab. Stat. 30 (1), 91-106, 2016.
• [25] A.A. Olosunde, On exponential power distribution and poultry feeds data: a case study, J. Iran. Stat. Soc. (JIRSS) 12 (2), 253-270, 2013.
• [26] A. Parsian and N.S. Farsipour, Estimation of the mean of the selected population under asymmetric loss function, Metrika 50 (2), 89-107, 1999.
• [27] J. Putter and D. Rubinstein, On estimating the mean of a selected population, Technical Report No. 165, Department of Statistics, University of Wisconsin, 1968.
• [28] H.B. Sackrowitz and E. Samuel-Cahn, Evaluating the chosen population: a Bayes and minimax approach, in: Adaptive Statistical Procedures and Related Topics, Lecture Notes - Monograph Series 8, 386399, 1986.
• [29] N. Stallard, S. Todd and J. Whitehead, Estimation following selection of the largest of two normal means, J. Statist. Plann. Inference 138 (6), 1629-1638, 2008.
• [30] P. Vellaisamy, A note on unbiased estimation following selection, Stat. Methodol. 6 (4), 389-396, 2009.
• [31] P. Vellaisamy and A.P. Punnen, Improved estimators for the selected location parameters, Statist. Papers 43 (2), 291-299, 2002.
• [32] A. Zellner, Bayesian estimation and prediction using asymmetric loss functions, J. Amer. Statist. Assoc. 81 (394), 446-451, 1986.