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Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
In statistics, the delta method is a method of deriving the asymptotic distribution of a random variable. It is applicable when the random variable being considered can be defined as a differentiable function of a random variable which is asymptotically Gaussian .
In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n → ∞ .
Asymptotic analysis is a key tool for exploring the ordinary and partial differential equations which arise in the mathematical modelling of real-world phenomena. [3] An illustrative example is the derivation of the boundary layer equations from the full Navier-Stokes equations governing fluid flow.
V-statistics are a class of statistics named for Richard von Mises who developed their asymptotic distribution theory in a fundamental paper in 1947. [1] V-statistics are closely related to U-statistics [ 2 ] [ 3 ] (U for " unbiased ") introduced by Wassily Hoeffding in 1948. [ 4 ]
In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unmeasured correlation between observations from different timepoints.
For example, in estimating SUR model of 6 equations with 5 explanatory variables in each equation by Maximum Likelihood, the number of parameters declines from 51 to 30. [ 9 ] Despite its appealing feature in computation, concentrating parameters is of limited use in deriving asymptotic properties of M-estimator. [ 10 ]
In statistics, Hodges' estimator [1] (or the Hodges–Le Cam estimator [2]), named for Joseph Hodges, is a famous counterexample of an estimator which is "superefficient", [3] i.e. it attains smaller asymptotic variance than regular efficient estimators.