Score test under a simple null

Under a regular simple

p

-parameter null, the normalized score converges to

N_{p} (0, I_{1})

, so its information-standardized squared norm converges to

χ_{p}^{2}

.

Table of contents
- Quadratic form of a standard normal vector Score test under a simple null

Quadratic form of a standard normal vector

If

Z \sim N_{p} (0, I_{p})

, then

Z^{T} Z = \sum_{j = 1}^{p} Z_{j}^{2} \sim χ_{p}^{2}

.

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