Understanding the Delta Method


The Delta Method Requires Us To Find/Compute 4 Things

1) A parameter for which we know the variance - $\theta$

2) The variance of the paramter - $Var[\theta]$

2) A function of the parameter - $g(\theta)$

3) The partial derivatives - $\frac{\partial g(\theta)}{\partial \theta_{i}}, \;\; i=1,...m$

The General Delta Method Equation

$$ Var\left[g(\hat{\theta})\right]\approx \sum_{i=1}^{r} \left[\frac{\partial g(\mathbf{\theta})}{\partial \theta_{i}}\right]^{2} Var(\hat{\theta_{i}})+\sum_{i=1}^r \mathop{\sum^{r}{j=1}}{i\ne j}\left[\frac{\partial g(\mathbf{\theta})}{\partial \theta_{i}}\right]\left[\frac{\partial g(\mathbf{\theta})}{\partial \theta_{j}}\right] Cov(\hat{\theta}{i}, \hat{\theta}{j}) $$

Try the teachingApps package in your browser

Any scripts or data that you put into this service are public.

teachingApps documentation built on July 1, 2020, 5:58 p.m.