Shrinkage Estimators of the Probability Density Function and their Asymptotic Properties under Association

In the present article, we develop the well-known preliminary test and Stein- type estimators for the probability density function under association. In this respect, we derive the asymptotic characteristics of the proposed estimators under a set of local alternatives. Some numerical studies are provided for supporting the findings. The result of this article improves the kernel estimate of the marginal probability density function of a strictly stationary sequence of associated random variables. For practical sake, the behavior of the proposed estimators is also analyzed using a real data set.