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The weighted median is shown in red and is different than the ordinary median. In statistics, a weighted median of a sample is the 50% weighted percentile. [1] [2] [3] It was first proposed by F. Y. Edgeworth in 1888. [4] [5] Like the median, it is useful as an estimator of central tendency, robust against outliers. It allows for non-uniform ...
In statistics, the Hodges–Lehmann estimator is a robust and nonparametric estimator of a population's location parameter.For populations that are symmetric about one median, such as the Gaussian or normal distribution or the Student t-distribution, the Hodges–Lehmann estimator is a consistent and median-unbiased estimate of the population median.
For example: If L = (2, 2, 2, 3, 3, 4, 8, 8), then L' consists of six 2's, six 3's, four 4's, and sixteen 8's. That is, L' has twice as many 2s as L; it has three times as many 3s as L; it has four times as many 4s; etc. The median of the 32-element set L' is the average of the 16th smallest element, 4, and 17th smallest element, 8, so the N50 is
For context, the best single point estimate by L-estimators is the median, with an efficiency of 64% or better (for all n), while using two points (for a large data set of over 100 points from a symmetric population), the most efficient estimate is the 27% midsummary (mean of 27th and 73rd percentiles), which has an efficiency of about 81% ...
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated.This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators.
A winsorized mean is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean.It involves the calculation of the mean after winsorizing — replacing given parts of a probability distribution or sample at the high and low end with the most extreme remaining values, [1] typically doing so for an equal amount of both ...
An estimator for the slope with approximately median rank, having the same breakdown point as the Theil–Sen estimator, may be maintained in the data stream model (in which the sample points are processed one by one by an algorithm that does not have enough persistent storage to represent the entire data set) using an algorithm based on ε-nets.
A kernel smoother is a statistical technique to estimate a real valued function: as the weighted average of neighboring observed data. The weight is defined by the kernel, such that closer points are given higher weights. The estimated function is smooth, and the level of smoothness is set by a single parameter.