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Survey methodology textbooks generally consider simple random sampling without replacement as the benchmark to compute the relative efficiency of other sampling approaches. [3] An unbiased random selection of individuals is important so that if many samples were drawn, the average sample would accurately represent the population.
Reservoir sampling is a family of randomized algorithms for choosing a simple random sample, without replacement, of k items from a population of unknown size n in a single pass over the items. The size of the population n is not known to the algorithm and is typically too large for all n items to fit into main memory .
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 ...
A random sample can be thought of as a set of objects that are chosen randomly. More formally, it is "a sequence of independent, identically distributed (IID) random data points." In other words, the terms random sample and IID are synonymous. In statistics, "random sample" is the typical terminology, but in probability, it is more common to ...
Suppose marbles are drawn without replacement until the urn is empty. Let be the indicator random variable of the event that the -th marble drawn is red. Then {} =, …, + is an exchangeable sequence. This sequence cannot be extended to any longer exchangeable sequence.
Subsampling is an alternative method for approximating the sampling distribution of an estimator. The two key differences to the bootstrap are: the resample size is smaller than the sample size and; resampling is done without replacement. The advantage of subsampling is that it is valid under much weaker conditions compared to the bootstrap.
In probability theory and statistics, the negative hypergeometric distribution describes probabilities for when sampling from a finite population without replacement in which each sample can be classified into two mutually exclusive categories like Pass/Fail or Employed/Unemployed. As random selections are made from the population, each ...
Note that the inequalities also hold when the X i have been obtained using sampling without replacement; in this case the random variables are not independent anymore. A proof of this statement can be found in Hoeffding's paper. For slightly better bounds in the case of sampling without replacement, see for instance the paper by Serfling (1974).