# Bonferroni confidence region for shifted Laplace parameters

Consider the shifted Laplace distribution with the density:

$$f(y)=\frac{\theta}{2}e^{-\theta|y-\mu|}\quad, \quad y\in \mathbb R$$

Using the Bonferroni method, construct a $$100(1-\alpha)\%$$ confidence region for $$(\mu,\theta)$$.

I've only been able to find one pivot: $$2\theta\sum_i{|y_i-\mu|}\sim \chi^2_{2n}$$

I can't seem to find another pivot or some other asymptotic to construct a second confidence interval. Any help?