ABSTRACT
By a complex survey, we mean one in which any scheme of sampling other than simple random sampling (SRS) with replacement (WR) or without replacement (WOR) is employed; a common name for these two SRS schemes will be adopted as epsem, that is, equal probability selection methods. Estimating population totals or means involves weighting the sample observations using design parameters. Estimators for totals and means that are of practical uses are linear in observations on the values of the variables of interest. For such linear functions of single variables, variances or mean square errors (MSE) are quadratic forms, and suitable sample-based estimators for them are easily found, as we have discussed and illustrated in the preceding chapters. But the problem no longer remains so simple if we intend to estimate nonlinear functions of totals or means of more than one variable. In such cases, estimators that are linear functions of observations on more than one variable are not usually available, but nonlinear functions become indispensable. Their variances or MSEs, however, are difficult to express in simple exact forms, and
estimators thereof with desirable properties and simple cosmetic forms are not easy to work out. To get over these situations, alternative techniques are needed, and the following sections give a brief account of them.
