  This paper investigates the problem of estimating the larger location
parameter of two general location families from a decision-theoretic
perspective. In this estimation problem, we use the criteria of minimizing the
risk function and the Pitman closeness under a general bowl-shaped loss
function. Inadmissibility of a general location and equivariant estimators is
provided. We prove that a natural estimator (analogue of the BLEE of unordered
location parameters) is inadmissible, under certain conditions on underlying
densities, and propose a dominating estimator. We also derive a class of
improved estimators using the Kubokawa's IERD approach and observe that the
boundary estimator of this class is the Brewster-Zidek type estimator.
Additionally, under the generalized Pitman criterion, we show that the natural
estimator is inadmissible and obtain improved estimators. The results are
implemented for different loss functions, and explicit expressions for the
dominating estimators are provided. We explore the applications of these
results to for exponential and normal distribution under specified loss
functions. A simulation is also conducted to compare the risk performance of
the proposed estimators. Finally, we present a real-life data analysis to
illustrate the practical applications of the paper's findings.
