Abstract :
This paper shows that the finite-dimensional parameters of a monotone-index model
can be estimated by minimizing an objective function based on sorting the data+
The key observation guiding this procedure is that the sum of distances between
pairs of adjacent observations is minimized ~over all possible permutations! when
the observations are sorted by their values+ The resulting estimator is a generalization
of Cavanagh and Sherman’s monotone rank estimator ~MRE! ~Cavanagh
and Sherman, 1998, Journal of Econometrics 84, 351–381! and does not require
a bandwidth choice+ The estimator is Mn-consistent and asymptotically normal
with a consistently estimable covariance matrix+ This least-squares estimator can
also be used to estimate monotone-index panel data models+ AMonte Carlo study
is presented where the proposed estimator is seen to dominate the MRE in terms
of mean-squared error and mean absolute deviation+
