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Everything about Variance function

Smooth function in statistics

In statistics, the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean. The variance function is a measure of heteroscedasticity and plays a large role in many settings of statistical modelling. It is a main ingredient in the generalized linear model framework and a tool used in non-parametric regression, semiparametric regression and functional data analysis. In parametric modeling, variance functions take on a parametric form and explicitly describe the relationship between the variance and the mean of a random quantity. In a non-parametric setting, the variance function is assumed to be a smooth function. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Variance functionA 5-minute orientation
  2. Skim a recent paper: Variance reduction function for a potential inclined slip line in a spatially variable soilInfluential work since 2022
  3. Pick up a classic book: Cramer-von Mises variance estimators for simulationsThe most-reprinted book on the subject
  4. Read the landmark paper: Predicting the effects of coding non-synonymous variants on protein function using the SIFT algorithmCited 5,902 times
  5. Go sideways: Cramér–Rao boundA closely related topic
  6. Go sideways: Generalized functional linear modelA closely related topic

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