Anscombe Residual

Definition

Anscombe Transformation

$A(x)=\int V^{-1/3}(x)dx$ where $V$ is the variance function.

Anscombe Residual

The Anscombe residual is the Anscombe Transformed Pearson Residual. The transformation make the residual follows a normal distribution. $r_{A_i}=\frac{A(y_i)-A({\hat{\mu }}_i)}{\sqrt{V(A({\hat{\mu }}_i))}}=\frac{A(y_i)-A({\hat{\mu }}_i)}{A^{\prime }({\hat{\mu }}_i)\sqrt{V({\hat{\mu }}_i)}}$ where $\hat{\mu }=\mu (\theta )=b^{\prime }(\theta )$, $V(\hat{\mu })=b^{\prime \prime }(\theta )$ is the variance function.