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A cheat sheet for statistical estimators
What distribution and parameters fit our data? What is the confidence interval of the estimated parameters?
The above article contains the formulas with minimal explanations. If you have seen this topic some time ago, it is probably a good way to refresh memories. However, this would be a bit too harsh to start from scratch with it. This is, for a big part, formulas from my notes of the course at the DSTI, as we had an excellent teacher, with some parts from other sources.
Hypothesis and notations
- X is a random variable
- x is a realization of this random variable
- f is the associated density function
- F is the associated cumulative distribution function
- g and h are any functions of X
- i, j, k, n are integers
- θ in an unknown parameter
- θ̂ₙ is an estimator of θ according to X₁, … Xₙ. It is a random variable.
- A specific realization of θₙ according to the observations is referred to as an estimation.
