Interruption Estimation in Sequence of GCRD under Precautionary Loss Function

Uma Srivastava, Harish Kumar

Abstract: Change-points divide statistical models into homogeneous segments. Inference about change-points is discussed in many researches in the context of testing the hypothesis of ?no change?, point and interval estimation of a change-point, changes in nonparametric models, changes in regression, and detection of change in distribution of sequentially observed data. In this paper we consider the problem of single change-point estimation in the mean of a Generalized Compound Rayleigh Distribution under Precautionary Loss Function. We propose a robust estimator of parameter. Then, we propose to follow the classical inference approach, by plugging this estimator in the criteria used for change-points estimation. We show that the asymptotic properties of these estimators are the same as those of the classical estimators in the independent framework. This method is implemented in the R package for Comprehensive numerical study. This package is used in the simulation section in which we show that for finite sample sizes taking into account the dependence structure improves the statistical performance of the change-point estimators and of the selection criterion.

Keywords: Change Point Estimation, Generalized Compound Rayleigh Distribution. Bayesian method, Natural Conjugate Inverted Gamma Prior, Precautionary Loss Function