Abstract
Under classical survey sampling theory the errors mainly studied in the estimation are sampling errors. However, often non-sampling errors are more influential to the properties of the estimator than sampling errors. This is recognized by practitioners, researchers and many great works of literature regarding non-sampling errors have been published during last two decades, especially regarding non-response error which is one of the cornerstones of the non-sampling errors. The literature handles one kind of non-sampling error at a time, although in real surveys more than one non-sampling error is usually present.In this paper, two kinds of non-sampling errors are considered at the estimation stage: non-response and measurement error. An exponential ratio type estimator has been developed to estimate the population mean of the response variable in the presence of non-response and measurement errors. Theoretically and empirically, it has been shown that the proposed estimator is more efficient than usual unbiased estimator and other existing estimators.
Highlights
Design based estimation methods use the sampling distribution that results when the values for the finite population units are considered to be fixed, and the variation of the estimates arises from the fact that statistics are based on a random sample drawn from the population rather than a census of the entire population
We have proposed exponential ratio type estimator in the situation where non-response and measurement errors are present in both study variable and auxiliary variable
From Table 5; it is envisaged that the proposed estimator at its optimum performs more efficiently than the usual unbiased estimator, Shalabh’s (t1) and Shukla et al (t2) estimators for estimating the population mean in the presence of measurement error
Summary
Design based estimation methods use the sampling distribution that results when the values for the finite population units are considered to be fixed, and the variation of the estimates arises from the fact that statistics are based on a random sample drawn from the population rather than a census of the entire population, (see, Kish 1954, Sarndal, Swensson & Wretman 1992, Kish 1994, Gregoire 1998, Koch & Gillings 2006, Binder 2008, Dorazio 1999, Shabbir, Haq & Gupta 2014). (2003), Singh & Karpe (2007), Singh & Karpe (2008), Singh & Karpe (2009), Singh & Karpe (2010), (Gregoire & Salas 2009, Salas & Gregoire 2010), Shukla, Pathak & Thakur (2012), and Sharma & Singh (2013), etc Another problem the researcher faces is due to non-response which refers to the failure to collect information from one or more respondents on one or more variables. Jackman (1999) dealt with both non-response and measurement error simultaneously, in the case of voter turnout, where a reasonably large body of vote validation studies supply auxiliary information, allowing the components of bias in survey estimates of turnout rates to be isolated. An empirical study is carried out to show the efficiency of our suggested estimators over some available estimators
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