Premium
Sampling with probabilities proportional to the variable of interest
Author(s) -
Moors J. J. A.,
Smeets R.,
Boekema F. W. M.
Publication year - 1998
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00073
Subject(s) - estimator , mathematics , statistics , bias of an estimator , variance (accounting) , consistent estimator , sample (material) , sampling (signal processing) , minimum variance unbiased estimator , context (archaeology) , variable (mathematics) , econometrics , computer science , paleontology , mathematical analysis , chemistry , accounting , filter (signal processing) , chromatography , business , computer vision , biology
To estimate the mean sojourn time, a sample of Tilburg fair visitors was asked for the duration of their stay on the fair grounds. The longer a visitor's sojourn, the larger his/her probability of being interviewed will be; therefore, longer sojourn times will be overrepresented in the sample. As a consequence, the arithmetic sample mean is not a good estimator. The paper places this problem against a theoretical background. Sampling with unequal probabilities is considered in a general context. The special case that the sampling probabilities are a function of the variable under investigation, is discussed in detail. As a better estimator the harmonic mean of the observations is presented. Most properties of this estimator are difficult to derive analytically, but a suitable variance estimator is derived. The behavior of estimator and variance estimator is studied in a number of quite different examples.