Definition:Information Matrix

Definition

Let $\theta_1, \theta_2, \ldots, \theta_p$ be parameters

Let $S$ be a sample of $n$ observations from a probability distribution with frequency function $\map f {x, \theta_i}$.

The information matrix is a square matrix of order $p$ such that the $\tuple {i, j}$th element is given by:

$n \map E {\paren {\dfrac {\partial \ln f} {\partial \theta_i} } \paren {\dfrac {\partial \ln f} {\partial \theta_j} } }$

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Also see

• Results about information matrices can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): information: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): information: 2.