Matrices Used in Statistics
The following matrices find their main application in statistics and probability theory.
- Bernoulli matrix — a square matrix with entries +1, −1, with equal probability of each.
- Centering matrix — a matrix which, when multiplied with a vector, has the same effect as subtracting the mean of the components of the vector from every component.
- Correlation matrix — a symmetric n×n matrix, formed by the pairwise correlation coefficients of several random variables.
- Covariance matrix — a symmetric n×n matrix, formed by the pairwise covariances of several random variables. Sometimes called a dispersion matrix.
- Dispersion matrix — another name for a covariance matrix.
- Doubly stochastic matrix — a non-negative matrix such that each row and each column sums to 1 (thus the matrix is both left stochastic and right stochastic)
- Fisher information matrix — a matrix representing the variance of the partial derivative, with respect to a parameter, of the log of the likelihood function of a random variable.
- Hat matrix - a square matrix used in statistics to relate fitted values to observed values.
- Precision matrix — a symmetric n×n matrix, formed by inverting the covariance matrix. Also called the information matrix.
- Stochastic matrix — a non-negative matrix describing a stochastic process. The sum of entries of any row is one.
- Transition matrix — a matrix representing the probabilities of conditions changing from one state to another in a Markov chain
Read more about this topic: List Of Matrices
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“O for a man who is a man, and, as my neighbor says, has a bone in his back which you cannot pass your hand through! Our statistics are at fault: the population has been returned too large. How many men are there to a square thousand miles in this country? Hardly one.”
—Henry David Thoreau (1817–1862)