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The best example of the plug-in principle, the bootstrapping method. Bootstrapping is a statistical method for estimating the sampling distribution of an estimator by sampling with replacement from the original sample, most often with the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean, median, proportion, odds ratio ...
The bootstrap sample is taken from the original by using sampling with replacement (e.g. we might 'resample' 5 times from [1,2,3,4,5] and get [2,5,4,4,1]), so, assuming N is sufficiently large, for all practical purposes there is virtually zero probability that it will be identical to the original "real" sample. This process is repeated a large ...
Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement. Sampling done without replacement is no longer independent, but still satisfies exchangeability , hence most results of mathematical statistics still hold.
Schematic of Jackknife Resampling. In statistics, the jackknife (jackknife cross-validation) is a cross-validation technique and, therefore, a form of resampling.It is especially useful for bias and variance estimation.
The pps sampling results in a fixed sample size n (as opposed to Poisson sampling which is similar but results in a random sample size with expectancy of n). When selecting items with replacement the selection procedure is to just draw one item at a time (like getting n draws from a multinomial distribution with N elements, each with their own ...
A sample subset containing minimal number of data items is randomly selected from the input dataset. A fitting model with model parameters is computed using only the elements of this sample subset. The cardinality of the sample subset (e.g., the amount of data in this subset) is sufficient to determine the model parameters.
Let a be the value of our statistic as calculated from the full sample; let a i (i = 1,...,n) be the corresponding statistics calculated for the half-samples. (n is the number of half-samples.) Then our estimate for the sampling variance of the statistic is the average of (a i − a) 2. This is (at least in the ideal case) an unbiased estimate ...
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 ...