Second order asymptotic comparison of estimators of a common parameter in the double exponential case (Q1091057)

Let \(X_{i1},X_{i2},...,X_{in}\), \(i=1,2,...,m\), be m sets of independent samples each of size n, and for each i let \(X_{ij}\) have the following density function, \(j=1,...,n:\) \[ f(x,\theta,\tau_ i) = (1/2\pi i)\exp (-| X-\theta | /\tau_ i),\quad -\infty <x<\infty, \] where \(\theta\) is estimated and \(\tau_ i\) is a nuisance parameter and both are real and positive parameters. The author obtains the asymptotic expansions of the distributions of such estimators of \(\theta\) for maximum likelihood estimators, the weighted median and the weighted mean, and asymptotically compares them to the second order, i.e. the order \(n^{-}\).