Читать книгу Sampling and Estimation from Finite Populations - Yves Tille - Страница 42

Since

the bias of the estimator is

The bias is zero if and only if for all

If some inclusion probabilities are zero, it is impossible to estimate without bias. It is said that the sampling design does not cover the population or is vitiated by a coverage problem. We sometimes hear that a sample is biased, but this terminology should be avoided because bias is a property of an estimator and not of a sample. In what follows, we will consider that all the sampling designs have nonzero first‐order inclusion probabilities.