Modified Classes of Regression-Type Estimators of Population Mean in the Presences of Auxiliary Attribute

Abstract

The use of relevant information from auxiliary variable at the estimation stage and design stage to obtain reliable and efficient estimate is a common practice is a sample survey. But situations arise when the available auxiliary information are attribute in nature. There are some existing estimators based on auxiliary attribute in literature, however, they are less efficient when the bi-serial correlation between the study variable and auxiliary attribute is negative. Also, some depend on an unknown parameter of the study variable (Cy) which makes their applicability of the estimators in real life situations not possible unless if the value is estimated using a large sample which requires additional resources. In this work, the concept of regression base estimator was used to obtain estimators that are independent of unknown population parameter of the study variable and applicable for both negative and positive correlations. The properties (Biases and MSEs) of the modified estimators were derived up to the first order of approximation using Taylor series approach. The efficiency conditions of the proposed estimation over the existing estimator considered in the study were established. The empirical studies were conducted using both existing population parameters and stimulation to investigate the efficiency of the proposed estimators over the efficiency of the existing estimators. The results revealed that the proposed estimators have minimum MSEs and higher PREs among all the competing estimators. These imply that the proposed estimators are more efficient and can produce better estimate of the population mean compared to other existing estimators considered in the study.

Improved Modified Classes of Regression Type Estimators of Finite Population Mean in the Presence of Auxiliary Attribute

“…In this research, we proposed an improved modified regression estimators for the estimation of population mean in the presence of auxiliary attribute. The results of the empirical study revealed that the proposed estimators are more efficient than sample mean and Audu et al 1 estimators. This implies that the proposed estimators have great chance of producing precise estimate.…”

“…Table 4 shows MSEs and PREs of the suggested and some existing estimators using dataset 2. The result shows that the suggested estimators have minimum MSEs and higher PREs compared to the conventional estimators and Audu et al 1 estimators.…”

“…By exploiting the idea of Audu et al 1 Differentiating (26) with respect to u i and v i , equate to zero and solve for u i and v i simultaneously, we obtain and .…”

“…The 1 t pi and T qi , and suggested estimators, T ri and T qi estimators, considering two data sets respectively. The results revealed that the suggested estimators T ri and T qi have minimum MSEs and higher PREs as compared to the sample mean, Audu et al 1 estimators.…”

“…Other researchers that developed estimators using auxiliary information include. Audu et al, 1 Tailor et al, 11 Singh, 6,7 Kadilarand Cingi, 3 Khoshnevisan et al, 4 Perri, 5 Yunusa et al, 12 Singh and Kumar. 8 When the auxiliary information are qualitative in nature, that is, auxiliary information in the form of attribute, such as colour of hair of individuals and their weight can be regarded as auxiliary attribute and study variable, sex and height of women in a locality may be regarded as auxiliary attribute and study variable etc.…”