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An example arises in the estimation of the population variance by sample variance. For a sample size of n, the use of a divisor n−1 in the usual formula (Bessel's correction) gives an unbiased estimator, while other divisors have lower MSE, at the expense of
Data reduction is the transformation of numerical or alphabetical digital information derived empirically or experimentally into a corrected, ordered, and simplified form. . The purpose of data reduction can be two-fold: reduce the number of data records by eliminating invalid data or produce summary data and statistics at different aggregation levels for various applications
Jenks used the analogy of a “blanket of error” to describe the need to use elements other than the mean to generalize data. The three dimensional models were created to help Jenks visualize the difference between data classes. His aim was to generalize the data using as few planes as possible and maintain a constant “blanket of error”.
The variance of randomly generated points within a unit square can be reduced through a stratification process. In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. [1]
In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso, LASSO or L1 regularization) [1] is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the resulting statistical model.
The sample mean is thus more efficient than the sample median in this example. However, there may be measures by which the median performs better. For example, the median is far more robust to outliers , so that if the Gaussian model is questionable or approximate, there may advantages to using the median (see Robust statistics ).
His work in developing analysis of variance (ANOVA) set the groundwork for grouping experimental units to control for extraneous variables. Blocking evolved over the years, leading to the formalization of randomized block designs and Latin square designs. [ 1 ]
In statistics, Bessel's correction is the use of n − 1 instead of n in the formula for the sample variance and sample standard deviation, [1] where n is the number of observations in a sample. This method corrects the bias in the estimation of the population variance.