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?


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