Replacement of Selected Units
Sampling schemes may be without replacement ('WOR' - no element can be selected more than once in the same sample) or with replacement ('WR' - an element may appear multiple times in the one sample). For example, if we catch fish, measure them, and immediately return them to the water before continuing with the sample, this is a WR design, because we might end up catching and measuring the same fish more than once. Another example, the re-sampling process of a dataset of (n) years can be represented by having (n) balls of different colors in a box. Essentially, bootstrap re-sampling with replacement is to randomly pick a ball from the box, record its color and return the ball to the box. This process is repeated many times until a new time series is generated out of the original sample, the box of colored balls. However, if we do not return the fish to the water (e.g. if we eat the fish), this becomes a WOR design.
Read more about this topic: Random Selection
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