**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3

# auxiliary variable Related Publications

##### 3 On Optimum Stratification

**Authors:**
M. G. M. Khan,
V. D. Prasad,
D. K. Rao

**Abstract:**

In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

**Keywords:**
dynamic programming technique,
auxiliary variable,
nonlinear programming problem,
optimum stratification,
uniform distribution

##### 2 Adjusted Ratio and Regression Type Estimators for Estimation of Population Mean when some Observations are missing

**Authors:**
Nuanpan Nangsue

**Abstract:**

Ratio and regression type estimators have been used by previous authors to estimate a population mean for the principal variable from samples in which both auxiliary x and principal y variable data are available. However, missing data are a common problem in statistical analyses with real data. Ratio and regression type estimators have also been used for imputing values of missing y data. In this paper, six new ratio and regression type estimators are proposed for imputing values for any missing y data and estimating a population mean for y from samples with missing x and/or y data. A simulation study has been conducted to compare the six ratio and regression type estimators with a previous estimator of Rueda. Two population sizes N = 1,000 and 5,000 have been considered with sample sizes of 10% and 30% and with correlation coefficients between population variables X and Y of 0.5 and 0.8. In the simulations, 10 and 40 percent of sample y values and 10 and 40 percent of sample x values were randomly designated as missing. The new ratio and regression type estimators give similar mean absolute percentage errors that are smaller than the Rueda estimator for all cases. The new estimators give a large reduction in errors for the case of 40% missing y values and sampling fraction of 30%.

**Keywords:**
auxiliary variable,
missing data,
ratio and regression
type estimators

##### 1 New Product-Type Estimators for the Population Mean Using Quartiles of the Auxiliary Variable

**Authors:**
Amer Ibrahim Falah Al-Omari

**Abstract:**

In this paper, we suggest new product-type estimators for the population mean of the variable of interest exploiting the first or the third quartile of the auxiliary variable. We obtain mean square error equations and the bias for the estimators. We study the properties of these estimators using simple random sampling (SRS) and ranked set sampling (RSS) methods. It is found that, SRS and RSS produce approximately unbiased estimators of the population mean. However, the RSS estimators are more efficient than those obtained using SRS based on the same number of measured units for all values of the correlation coefficient.

**Keywords:**
auxiliary variable,
extreme ranked set sampling,
product estimator,
simple random
sampling