Sandeep Kumar’s scientific contributions

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Publications (3)


On various approaches for estimating finite population total in survey sampling under ratio super population model
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December 2017

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268 Reads

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2 Citations

International Journal of Agricultural and Statistical Sciences

Sandeep Kumar

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Sunil Kumar

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Deville and Särndal (1992) developed calibration estimator by using the auxiliary information to obtain a better estimate of the population total of study variate y. While calibration approach does not assume any explicit relationship between y and x but it assumes that only X, the population total of x is known. Prediction approach advocated by Royall and Herson (1973) leads to model based estimator of finite population under a assumption of specified super population model where xi's are supposed to be known for all i = 1, 2, 3, ..., N. Wu and Sitter (2001) proposed a design oriented model based calibration estimator of population total, when they also assumed that Xi are known for all i = 1, 2, 3, ..., N. It has been shown that these three approaches i.e. calibration approach, model based approach and model based calibration approach provides the same estimator under some situation. However, their variances are different. In the present paper, an attempt has been made to conduct a limited simulation study to examine the relative performance of the estimators based on the aforesaid three approaches. From the results of the simulation study, it has been found that calibration estimates are best.

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CALIBRATION APPROACH BASED ESTIMATION OF FINITE POPULATION TOTAL IN SURVEY SAMPLING UNDER SUPER POPULATION MODEL WHEN STUDY VARIABLE AND AUXILIARY VARIABLE ARE INVERSELY RELATED

December 2017

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191 Reads

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5 Citations

In the present paper we have developed calibration and model based calibration estimators of finite population total when study variable and auxiliary variable are inversely related. It has been shown that calibration, model based and model based calibration approaches provided the same estimators under certain conditions but their variances are different. A limited simulation study has been conducted to examine the relative performance of the estimators based on the aforesaid three approaches. The results of simulation study indicated that regression type model based calibration estimator is the best among all the estimators.


Citations (2)


... A model identified the set of conditions that describe a class of distribution of Y = {y 1 , y 2 , …, y N } [22]. Kumar et al. [23] proposed the model-based calibration estimator when the study and auxiliary variables are inversely related. We propose a model-based instrumental-variable calibration estimator of Y by the Instrumental-variable calibration approach proposed by Ref. [5] under the model given in equation (2.1) as: ...

Reference:

Integrating Endogeneity in Survey Sampling Using Instrumental-Variable Calibration Estimator
CALIBRATION APPROACH BASED ESTIMATION OF FINITE POPULATION TOTAL IN SURVEY SAMPLING UNDER SUPER POPULATION MODEL WHEN STUDY VARIABLE AND AUXILIARY VARIABLE ARE INVERSELY RELATED

... Note that the estimator in (2) is the usual ratio estimator when Sud et al. (2014) developed calibration approach based regression type estimator for inverse relationship between study and auxiliary variable. Recently, Sandeep Kumar et al. (2017) have studied the relative performance of various approaches of estimating population total under ratio super population model. In view of above discussion, an attempt has been made in the present paper to examine the relative performance of the estimators based on various approaches, i.e. (i) model based (ii) calibration approach based and (iii) model based calibration approach, when study and auxiliary variables are inversely related. ...

On various approaches for estimating finite population total in survey sampling under ratio super population model

International Journal of Agricultural and Statistical Sciences