Contents
What are sample estimators?
What is an Estimator? The sample mean is an estimator for the population mean. An estimator is a statistic that estimates some fact about the population. You can also think of an estimator as the rule that creates an estimate. For example, the sample mean(x̄) is an estimator for the population mean, μ.
What is a ratio sampling?
Sampling ratio is size of sample divided by size of population. Contrary to popular belief, a large sampling ratio is not crucial. Sampling frame is a specific list of names from which sample elements will be chosen.
Are ratio estimators biased?
The ratio estimators are biased. The bias occurs in ratio estimation because E(y/x) = E(y)/E(x) (i.e., the expected value of the ratio = the ratio of the expected values. When appropriately used, the reduction in variance from using the ratio estimator will offset the presence of bias.
How are ratio estimators used in random sampling?
This study proposes ratio estimators by adapting the estimators’ type of Ray and Singh [J. Ind. Stat. Assoc. 19 (1981) 147] to traditional and the other ratio-type estimators in simple random sampling in literature. Theoretically, mean square error (MSE) equations of all proposed ratio estimators are obtained and compared with each other.
How to calculate the variance of a ratio estimator?
Now, compute the estimated variance of the ratio estimator. where σ r 2 is the variance of Y about the ratio line. σ 2 is the variance of Y. σ r 2 can be estimated by s r 2 = ∑ i = 1 n ( y i − r x i) 2 n − 1 and σ 2 can be estimated by s 2 = ∑ i = 1 n ( y i − y ¯) 2 n − 1.
How is auxiliary information used in ratio method of estimation?
Use of such auxiliary information is made through the ratio method of estimation to obtain an improved estimator of population mean. In ratio method of estimation, auxiliary information on a variable is available which is linearly related to the variable under study and is utilized to estimate the population mean.
How are MSE equations used in ratio estimators?
Theoretically, mean square error (MSE) equations of all proposed ratio estimators are obtained and compared with each other. By these comparisons the conditions, which make each proposed estimator more efficient than the others, are found. The theoretical results are supported by a numerical illustration. 1. Introduction