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The problem of simultaneous estimation of order restricted locationparameters $\theta_1$ and $\theta_2$ ($-\infty<\theta_1\leq \theta_2<\infty$)of a bivariate location symmetric distribution, under a general loss function,is being considered. In the literature, many authors have studied this problemfor specific probability models and specific loss functions. In this paper, weunify these results by considering a general bivariate symmetric model and aquite general loss function. We use the Stein and the Kubokawa (or IERD)techniques to derive improved estimators over any location equivariantestimator under a general loss function. We see that the improved Stein typeestimator is robust with respect to the choice of a bivariate symmetricdistribution and the loss function, as it only requires the loss function tosatisfy some generic conditions. A simulation study is carried out to validatethe findings of the paper. A real-life data analysis is also provided.

A Note On Simultaneous Estimation of Order Restricted Location  Parameters of a General Bivariate Symmetric Distribution Under a General Loss  Function