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Mean imputation can be carried out within classes (i.e. categories such as gender), and can be expressed as ^ = ¯ where ^ is the imputed value for record and ¯ is the sample mean of respondent data within some class . This is a special case of generalized regression imputation:
Predictive mean matching (PMM) [1] is a widely used [2] statistical imputation method for missing values, first proposed by Donald B. Rubin in 1986 [3] and R. J. A. Little in 1988. [ 4 ] It aims to reduce the bias introduced in a dataset through imputation, by drawing real values sampled from the data. [ 5 ]
Data often are missing in research in economics, sociology, and political science because governments or private entities choose not to, or fail to, report critical statistics, [1] or because the information is not available. Sometimes missing values are caused by the researcher—for example, when data collection is done improperly or mistakes ...
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
In survey research, the design effect is a number that shows how well a sample of people may represent a larger group of people for a specific measure of interest (such as the mean). This is important when the sample comes from a sampling method that is different than just picking people using a simple random sample.
This simple example for the case of mean estimation is just to illustrate the construction of a jackknife estimator, while the real subtleties (and the usefulness) emerge for the case of estimating other parameters, such as higher moments than the mean or other functionals of the distribution.
For the variables under examination, analysts typically obtain descriptive statistics for them, such as the mean (average), median, and standard deviation. [61] They may also analyze the distribution of the key variables to see how the individual values cluster around the mean. [62] An illustration of the MECE principle used for data analysis.
First, when the NMF components are known, Ren et al. (2020) proved that impact from missing data during data imputation ("target modeling" in their study) is a second order effect. Second, when the NMF components are unknown, the authors proved that the impact from missing data during component construction is a first-to-second order effect.