On Sampling with Varying Probabilities

Abstract

When some sample observations are missing, the R.H.C. estimate of the population total, based on the available observations, is not unbiased. A corresponding unbiased estimate has been considered which shows a considerable increase in its variance. Two alternatives to the R.H.C. scheme are proposed and the corresponding estimation procedures have been developed. The two proposed estimates are compared with the unbiased estimate corresponding to the R.H.C. scheme with and without missing observations under the well known Cochran’s finite population model. It is found that in some situations the proposed schemes provide better estimates than the R.H.C. scheme. The unbiased estimate of the population total under the R.H.C. scheme with missing observations is also compared with the corresponding ratio estimate as deprived from a simple random sample. It is seen that ratio estimate is more efficient than the R.H.C. estimate when g < 1 and also when g is slightly greater than unity and p is sufficiently high.