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Multiple imputation can be used in cases where the data are missing completely at random, missing at random, and missing not at random, though it can be biased in the latter case. [14] One approach is multiple imputation by chained equations (MICE), also known as "fully conditional specification" and "sequential regression multiple 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 ]
The data imputation procedure with NMF can be composed of two steps. 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.
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.
Candès and Recht [3] proved that with assumptions on the sampling of the observed entries and sufficiently many sampled entries this problem has a unique solution with high probability. An equivalent formulation, given that the matrix M {\displaystyle M} to be recovered is known to be of rank r {\displaystyle r} , is to solve for X ...
For example, let the design effect, for estimating the population mean based on some sampling design, be 2. If the sample size is 1,000, then the effective sample size will be 500. It means that the variance of the weighted mean based on 1,000 samples will be the same as that of a simple mean based on 500 samples obtained using a simple random ...
If we associate with each item of the input a uniformly generated random number, the k items with the largest (or, equivalently, smallest) associated values form a simple random sample. [3] A simple reservoir-sampling thus maintains the k items with the currently largest associated values in a priority queue.
GPR is a Bayesian non-linear regression method. A Gaussian process (GP) is a collection of random variables, any finite number of which have a joint Gaussian (normal) distribution. A GP is defined by a mean function and a covariance function, which specify the mean vectors and covariance matrices for each finite collection of the random variables.