Generalized Classes of Regression-Cum-Ratio Estimators of Population Mean in Stratified Random Sampling
- PDF / 240,952 Bytes
- 7 Pages / 595.276 x 790.866 pts Page_size
- 52 Downloads / 238 Views
RESEARCH ARTICLE
Generalized Classes of Regression-Cum-Ratio Estimators of Population Mean in Stratified Random Sampling Manish Kumar1 • Gajendra K. Vishwakarma2
Received: 9 April 2017 / Revised: 30 January 2019 / Accepted: 6 June 2019 The National Academy of Sciences, India 2019
Abstract In this paper, classes of separate and combined regression-cum-ratio estimators have been proposed for estimating the finite population mean in stratified random sampling. The expressions for biases and mean square errors (MSEs) of the proposed classes have been derived to the first order of approximation. It has also been verified that the proposed classes of estimators, at their optimum conditions, are equivalent to the separate regression estimator. The proposed classes of estimators have been compared with the other existing estimators using MSE criterion, and the conditions under which the proposed classes perform better have been obtained. Numerical illustrations are given in support of theoretical findings. Relevance of the work The estimation theory is relevant to various interdisciplinary areas of research including economics, clinical trials, population studies, engineering, agriculture, etc. Also, the problem of estimation of mean is of huge importance in research, for instance, the estimation of: average agricultural production, average life span of persons in a region, mean concentration of dissolved minerals in water, and much more. For the estimation of mean, several design-based approaches are being widely used, for instance, simple random sampling, stratified random sampling, two-phase sampling, etc. If the population under study is homogeneous, then the simple random & Manish Kumar [email protected] Gajendra K. Vishwakarma [email protected] 1
Department of Mathematics, Birla Institute of Technology, Mesra 835215, India
2
Department of Applied Mathematics, IIT (ISM), Dhanbad 826004, India
sampling design is used at the estimation stage. However, in various practical situations, the research study is based on the heterogeneous population, and in that case the stratified random sampling procedure is preferable over the simple random sampling. Considering the above fact, an attempt has been made in this paper to develop the classes of generalized estimators for the mean of the variable under study using stratified random sampling. Keywords Study variable Auxiliary variable Population mean Bias MSE Mathematics Subject Classification 62D05
1 Introduction The stratified random sampling procedure is commonly used in surveys dealing with estimation and inferential purposes when the units of a target population vary considerably. The procedure mainly consists of dividing members of the population into homogeneous subgroups, known as strata, and then selecting samples from each stratum utilizing various allocation schemes (for instance, equal allocation, proportional allocation, or optimum allocation) by the well-known method of simple random sampling. Some of the most common strata used in str
Data Loading...
